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Factoring Out GC= F
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To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).
Factoring Out GC= F
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To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be prime.
Factoring Out GC= F
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To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in t= he product is prime. = ;
Factoring Out GC= F
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Example A. Factor completely 12.=
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0161.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0162.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime, incomplete
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0162_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAG ABEAgAAAAAAAAAIVBBJmqMjnoJsRKttSvm9pz30YuAEFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0162_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJAAMAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQAAwAe AAYAgAAAAAAAAAIVhBFxy+2Y1Jst2ouz3lwbS4VOIooFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0156.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
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Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5,
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0163_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAG ABEAgAAAAAAAAAIVBBJmqMjnoJsRKttSvm9pz30YuAEFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0163_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQAa ABQAgAAAAAAAAAIuDI6pq+HPYntO2kPvpVVHbnhLmIlSaY5Qyqzs1L0IKmNxDdCyvt81zwIGfTtA AQA7 ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0164.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0164_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAG ABEAgAAAAAAAAAIVBBJmqMjnoJsRKttSvm9pz30YuAEFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0164_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQAa ABQAgAAAAAAAAAIuDI6pq+HPYntO2kPvpVVHbnhLmIlSaY5Qyqzs1L0IKmNxDdCyvt81zwIGfTtA AQA7 ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0165.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
b. The common factor of 4ab, 6a are
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0165_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAG ABEAgAAAAAAAAAIVBBJmqMjnoJsRKttSvm9pz30YuAEFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0165_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQAa ABQAgAAAAAAAAAIuDI6pq+HPYntO2kPvpVVHbnhLmIlSaY5Qyqzs1L0IKmNxDdCyvt81zwIGfTtA AQA7 ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0166.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
b. The common factor of 4ab, 6a are 2, =
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0166_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAG ABEAgAAAAAAAAAIVBBJmqMjnoJsRKttSvm9pz30YuAEFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0166_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQAa ABQAgAAAAAAAAAIuDI6pq+HPYntO2kPvpVVHbnhLmIlSaY5Qyqzs1L0IKmNxDdCyvt81zwIGfTtA AQA7 ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0167.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
b. The common factor of 4ab, 6a are 2, a,
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0167_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAG ABEAgAAAAAAAAAIVBBJmqMjnoJsRKttSvm9pz30YuAEFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0167_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQAa ABQAgAAAAAAAAAIuDI6pq+HPYntO2kPvpVVHbnhLmIlSaY5Qyqzs1L0IKmNxDdCyvt81zwIGfTtA AQA7 ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0168.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
b. The common factor of 4ab, 6a are 2, a, 2a.<= /span>
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0168_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAG ABEAgAAAAAAAAAIVBBJmqMjnoJsRKttSvm9pz30YuAEFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0168_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQAa ABQAgAAAAAAAAAIuDI6pq+HPYntO2kPvpVVHbnhLmIlSaY5Qyqzs1L0IKmNxDdCyvt81zwIGfTtA AQA7 ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0169.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
b. The common factor of 4ab, 6a are 2, a, 2a.&= #13;
c. The common factors of 6xy, 15x2y = are
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0169_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAG ABEAgAAAAAAAAAIVBBJmqMjnoJsRKttSvm9pz30YuAEFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0169_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQAa ABQAgAAAAAAAAAIuDI6pq+HPYntO2kPvpVVHbnhLmIlSaY5Qyqzs1L0IKmNxDdCyvt81zwIGfTtA AQA7 ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0170.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
b. The common factor of 4ab, 6a are 2, a, 2a.&= #13;
c. The common factors of 6xy, 15x2y = are 3,
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0170_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAG ABEAgAAAAAAAAAIVBBJmqMjnoJsRKttSvm9pz30YuAEFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0170_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQAa ABQAgAAAAAAAAAIuDI6pq+HPYntO2kPvpVVHbnhLmIlSaY5Qyqzs1L0IKmNxDdCyvt81zwIGfTtA AQA7 ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0171.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
b. The common factor of 4ab, 6a are 2, a, 2a.&= #13;
c. The common factors of 6xy, 15x2y = are 3, x,
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0171_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAG ABEAgAAAAAAAAAIVBBJmqMjnoJsRKttSvm9pz30YuAEFADs= ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0171_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQAa ABQAgAAAAAAAAAIuDI6pq+HPYntO2kPvpVVHbnhLmIlSaY5Qyqzs1L0IKmNxDdCyvt81zwIGfTtA AQA7 ------=_NextPart_01C8FD9E.79562D10 Content-Location: file:///C:/B15428C6/1factoringoutgcf_files/slide0172.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
b. The common factor of 4ab, 6a are 2, a, 2a.&= #13;
c. The common factors of 6xy, 15x2y = are 3, x, y2,
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
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Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
b. The common factor of 4ab, 6a are 2, a, 2a.&= #13;
c. The common factors of 6xy, 15x2y = are 3, x, y2, xy2, ..
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
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Example A. Factor completely 12.
12 =3D 3 * 4 =3D 3 * 2 * 2
not prime=
factored completely
To factor <= /span>means to = rewrite a quantity as a product (in a nontrivial way).  A quantity x that can’t be written as product besides as 1*x is said to be = prime. To factor completely means each factor in t= he product is prime. 
Factoring Out GC= F
Example B.
 =
a.  For 6 =3D 2*3, 15 =3D 3*5, 3 is a common factor.
b. The common factor of 4ab, 6a are 2, a, 2a.&= #13;
c. The common factors of 6xy, 15x2y = are 3, x, y2, xy2, ..
d. The common factor of a(x+y), b(x+y) is (x+y).
  
A = common factor of two or more quantities is a factor
belongs t= o all the quantities.
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36}
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36} =3D 12.
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36} =3D 12.
b. GCF{4ab, 6a}
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36} =3D 12.
b. GCF{4ab, 6a} =3D 2a.
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36} =3D 12.
b. GCF{4ab, 6a} =3D 2a. 
c. GCF {6xy2, 15 xy2}
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36} =3D 12.
b. GCF{4ab, 6a} =3D 2a. 
c. GCF {6xy2, 15 xy2} =3D 3xy.
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36} =3D 12.
b. GCF{4ab, 6a} =3D 2a. 
c. GCF {6xy2, 15 xy2} =3D 3xy.
d. GCF{x3y, x4y, x5y} =3D
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36} =3D 12.
b. GCF{4ab, 6a} =3D 2a. 
c. GCF {6xy2, 15 xy2} =3D 3xy.
d. GCF{x3y, x4y, x5y} =3D x3y.
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36} =3D 12.
b. GCF{4ab, 6a}, =3D 2a. 
c. GCF {6xy2, 15 xy2} =3D 3xy.
d. GCF{x3y, x4y, x5y} =3D x3y.
The Extraction Law
Distributive law interpreted backward gives the Extraction Law, that is, common factors may be extracted from sums or di= fferences.
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36} =3D 12.
b. GCF{4ab, 6a} =3D 2a. 
c. GCF {6xy2, 15 xy2} =3D 3xy.
d. GCF{x3y, x4y, x5y} =3D x3y.
The Extraction Law
Distributive law interpreted backward gives the Extraction Law, that is, common factors may be extracted from sums or di= fferences.
        = ;            &n= bsp;         AB ± AC à= ; A(B±C)
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The greatest common factor (GCF)= is the common factor that has the largest coefficient and highest degree of each factor among all common fact= ors.
Factoring Out GC= F
Example C. Find the GCF of the given quantities.
a. GCF{24, 36} =3D 12.
b. GCF{4ab, 6a} =3D 2a. 
c. GCF {6xy2, 15 xy2} =3D 3xy.
d. GCF{x3y, x4y, x5y} =3D x3y.
The Extraction Law
Distributive law interpreted backward gives the Extraction Law, that is, common factors may be extracted from sums or di= fferences.
        = ;            &n= bsp;         AB ± AC à= ; A(B±C)
This procedure is also called “factoring out common factor”.  To factor, the first step al= ways is to factor out the GCF.
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Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y
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(the GCF is y)
Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y    &nbs= p;
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(the GCF is y)
Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
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(the GCF is y)
Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a
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(the GCF is y)
(the GCF is 2a)
Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a
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(the GCF is y)
(the GCF is 2a)
Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a =3D 2a(2b) + 2a(3)
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(the GCF is y)
(the GCF is 2a)
Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a =3D 2a(2b) + 2a(3) =3D 2a(2b + 3)
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(the GCF is y)
(the GCF is 2a)
Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a =3D 2a(2b) + 2a(3) =3D 2a(2b + 3)
c. 12x2y3 + 6x2y2 
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(the GCF is y)
(the GCF is 2a)
(the GCF is 6x2y)
Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a =3D 2a(2b) + 2a(3) =3D 2a(2b + 3)
c. 12x2y3 + 6x2y2 
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(the GCF is y)
(the GCF is 2a)
(the GCF is 6x2y)
Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a =3D 2a(2b) + 2a(3) =3D 2a(2b + 3)
c. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + 6x2y= 2(1)
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(the GCF is y)
(the GCF is 2a)
(the GCF is 6x2y)
Factoring Out GC= F
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a =3D 2a(2b) + 2a(3) =3D 2a(2b + 3)
c. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + 6x2y= 2(1) =3D = 6x2y= 2(2y + 1)=
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Factoring Out GC= F
We may pull out common fac= tors that are (     &= nbsp; )'s.
(the GCF is y)
(the GCF is 2a)
(the GCF is 6x2y)
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a =3D 2a(2b) + 2a(3) =3D 2a(2b + 3)
c. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + 6x2y= 2(1) =3D = 6x2y= 2(2y + 1)=
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Factoring Out GC= F
We may pull out common fac= tors that are (     &= nbsp; )'s.
Example E. Factor
 
a. a(x + y) – 4(x + y)
(the GCF is y)
(the GCF is 2a)
(the GCF is 6x2y)
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a =3D 2a(2b) + 2a(3) =3D 2a(2b + 3)
c. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + 6x2y= 2(1) =3D = 6x2y= 2(2y + 1)=
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Factoring Out GC= F
We may pull out common fac= tors that are (     &= nbsp; )'s.
Example E. Factor
 
a. a(x + y) – 4(x + y)
    Pull out the common f= actor (x + y)
(the GCF is y)
(the GCF is 2a)
(the GCF is 6x2y)
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a =3D 2a(2b) + 2a(3) =3D 2a(2b + 3)
c. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + 6x2y= 2(1) =3D = 6x2y= 2(2y + 1)=
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Factoring Out GC= F
We may pull out common fac= tors that are (     &= nbsp; )'s.
Example E. Factor
 
a. a(x + y) – 4(x + y)
    Pull out the common f= actor (x + y)
    a(x + y) – 4(x + y) =3D = (x + y)(a – 4= )
(the GCF is y)
(the GCF is 2a)
(the GCF is 6x2y)
Example D. Factor out the GCF.
a. xy – 4y =3D y(x – 4)
    
b. 4ab + 6a =3D 2a(2b) + 2a(3) =3D 2a(2b + 3)
c. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + 6x2y= 2(1) =3D = 6x2y= 2(2y + 1)=
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