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Factoring
Polynomials
ARC INSTRUCTIONAL VIDEO
MAT 120
COLLEGE ALGEBRA
Factors

When an integer is written as a product of
integers, each of the integers in the product is a
factor of the original number

Factoring – writing a polynomial as a product of
polynomials.
Greatest Common Factor

Greatest common factor – largest quantity that is a
factor of all the integers or polynomials involved.

Finding the GCF of a list of integers or terms
 Prime
factor the numbers
 Identify
 Take
 If
common prime factors
the product of all common prime factors
there are no common prime factors, GCF is 1
Greatest Common Factor

Example:

Find the GCF of each list of numbers
 6x5 and 4x3
 6x5 = 2 · 3 · x · x · x · x · x
 4x3 = 2 · 2 · x · x · x
 So the GCF is 2 · x · x · x = 2x3
 12
and 8
 12 = 2 · 2 · 3
8=2·2·2
 So the GCF is 2 · 2 = 4.
Factoring Polynomials

The first step in factoring a polynomial is to find
the GCF of all its terms

Then we write the polynomial as a product by
factoring out the GCF from all the terms

The remaining factors in each term will form a
polynomial
Factoring out the GCF

Example:

Factor out the GCF in each of the following polynomials
 6x3 – 9x2 + 12x =
 3 · x · 2 · x2 – 3 · x · 3 · x + 3 · x · 4 =
 3x(2x2 – 3x + 4)
+ 2) – y(x + 2) =
 6 · (x + 2) – y · (x + 2) =
 (x + 2)(6 – y)
 6(x
Factoring

Remember that factoring out the GCF from the terms of a
polynomial should always be the first step in factoring a
polynomial.

This will usually be followed by additional steps in the process

Example:
 Factor
90 + 15y2 – 18x – 3xy2.
90 + 15y2 – 18x – 3xy2 = 3(30 + 5y2 – 6x – xy2) =
3(5 · 6 + 5 · y2 – 6 · x – x · y2) =
3(5(6 + y2) – x (6 + y2)) =
3(6 + y2)(5 – x)