finding the GCF of the polynomials

1. Factoring Polynomials
by Greatest Common Factor (GCF)
LARRY D. BUGARING
MALABON NATIONAL HIGH SCHOOL

2. Definitions
To factor an expression means to write an
equivalent expression that is a product
To factor a polynomial means to write the
polynomial as a product of other polynomials

3. Think of the Distributive Property of Equality:
a(b+c) = ab + ac  reverse it ab + ac = a(b + c)
To factor the GCF out of a polynomial, we do the following:
1. Find the GCF of all the terms in the polynomial.
2. Express each term as a product of the GCF and another factor.
3. Use the distributive property to factor out the GCF.

4. Let's factor the GCF out of 2x3-6x2
1. Find the GCF of all the terms in the polynomial.
2x3
6x2
= 2 * x * x * x
= 2 * 3 * x * x
GCF = 2x2
2. Express each term as a product of the GCF and another factor.
2x3
6x2
= (2x2)
= (2x2)
(x)
(3)

5. So the polynomial can be written as
2x3 - 6x2 = (2x2) (x) - (2x2)(3)
3. Factor out the GCF
Now we can apply the distributive property to factor out (2x2)
(2x2) (x) - (2x2)(3) = 2x2 (x – 3)
ab - ac = a(b - c)

6. Faster method
Once we know the GCF, the factored form is simply the
product of that GCF and the sum or difference of the
terms in the original polynomial divided by the GCF.
Find the factor of 5x2 + 10x
5x2
10x
= 5 * x * x
= 5 *2 * x
GCF = 5x
5x( 5x2 + 10x)5x 5x = 5x ( x + 2)

7. Your Turn
Find the factor form of the polynomials by GCF
1. 14x2y2z + 21xy2z2
2. 12w3t2 – 9wt2 + 15w2t3
Answer
1. 7xy2z (2x + 3z)
2. 3wt2 (4w2 – 3 + 5wt)