MCR 3U1
Unit 2
Lesson 3: Factoring Polynomials
You have already learned several methods for factoring including:
A: Finding a common factor
2x3  4x 2  6x
B: Factoring a trinomial in the form ax 2  bx  c where a  1
x 2  7 x  12
C: Factoring a trinomial in the form ax 2  bx  c where a  1 using decomposition/criss-cross
3x 2  4 x  1
D: Factoring a difference of squares
4 x 2  25 y 2
E: Factoring a perfect square trinomial
x 2  8 x  16
Factoring By Grouping
We need to use this method for polynomials which cannot be factored using one of the above
methods.
f ( x)  x 3  x 2  x  1
1. Group pairs of terms.
2. Factor the greatest common factor
from each pair.
3. Factor out the greatest common
factor, (x + 1), to complete the
factoring.
MCR 3U1
Unit 2
Example 1: Factor each of the following polynomials.
a) 6 x 2  2 xy  15 x  5 y
b) xm  xn  ym  yn
Factoring by Grouping as a Difference of Squares
Given the function below, we can factor using a familiar method previously discussed.
f ( x)  x 2  6 x  9  4 y 2
1. The first three terms are the square
of the binomial (x – 3). The last term
is the square of 2y.
2. The resulting expression is a
difference of squares.
Example 2: Factor each of the following polynomials.
a) a 2  b 2  8ac  16c 2
b) a 2  b 2  25  10a
Example 3: Sheila wants to paint the front of a rectangular door. The front of the door has an area
represented by the function A  2n 3  12n 2  3n  18 . Determine the expressions for the measures
of the length and width of the door. Show your work and describe how you found your answer.