Name ___________________________
Algebra I
Unit 8 Day 3
Date __________
 What is the Greatest Common Factor (GCF) of a polynomial?
It is the biggest _____________ and ____________ degree of variable that divides
exactly into each monomial of the given polynomial.
For example:
3 2
6 3
4
What is the GCF of 15 x y + 20 x y  10 x y




?
The greatest number that divides exactly into 15 , 20, and –10 is: ______
The smallest degree of x that “fits” into x3 , x 6 , and x 4 is: ________
The smallest degree of y that “fits” into y 2 , y 3 , and y is: ________
Therefore, the GCF for this polynomial is: _______
You try…
Find the GCF for the following polynomials.
a)
12 x 4  8 x3  4 x 2
b) 14ak 6  4a 2 k 3  8ak 4
 Sometimes the GCF doesn’t include a variable
Check if all monomials in the polynomial have at least one of the same variable.
If they don’t, then the GCF won’t include a variable part.
For example:
2
2
What is the GCF of 3a  12ab  9b
?
 The greatest number that divides exactly into 3 , –12, and 9 is: ______
 Monomials don’t all share at least one of the same variable , so no variable in
the GCF.
 Therefore, the GCF for this polynomial is: _____
You try…
Find the GCF for the following polynomials.
c)
18 pw3  24w2  12 p
d)
24d 2  16d  32d 3  8 j
 Sometimes the GCF doesn’t include a number other than 1
Sometimes the only factor that the coefficients in a polynomial have in common is the
number 1.
For example:
What is the GCF of 5 x 4  8 x3  2 x 2 ?
 The greatest number that divides exactly into 5 , 8, and –2 is: ______
4
3
 The smallest degree of x that “fits” into x , x , and x 2 is: ____
 Therefore, the GCF for this polynomial is: ____________
You try…
Find the GCF for the following polynomials.
e)
2 g  3g 5  11g 2  6 g 3
f)
15m3q3  7mq 2  22m4 q5
 Sometimes there is no GCF at all
If the only common numerical factor among all the coefficients is 1, and if the
monomials don’t all have at least one of the same variable, then there is no GCF
(other than the number 1).
For example:
What is the GCF of 7c 2  11c  14m ?
 The greatest number that divides exactly into 7 , –11, and –14 is: ______
 Monomials don’t all share at least one of the same variable , so no variable in
the GCF.
 Therefore, the GCF for this polynomial is: ____________
You try…
Which of the polynomials below has a GCF? If it has a GCF, say what it is.
g)
9 x5  12 gw2  7 gx
h)
10 y 2  3 y  8
i)
20 x 2  40 x