Section 5.7
Factoring by Special Products
Objectives:
• Factor a perfect square trinomial
• Factor the difference of two squares
Factor:
Factor the following:
What is the pattern?
Check?
Factor:
Check?
Factor the following:
What is the pattern?
Factoring Perfect Square Trinomials:
Perfect Square Trinomials
Factor the following: Check?
Something new?
Check?
Factor:
What is the pattern?
Difference of Squares:
Difference of Two Squares
Factor the following polynomials:
Check?
A Factoring Strategy:
1. Look for a common factor ﴾gcf﴿. If there is one, factor it out first.
2. Is the polynomial a binomial ﴾two terms﴿? If so, is it the difference of two squares?
Remember that the sum of two square is prime.
3. Is the polynomial a trinomial ﴾three terms﴿?
a. Is it a perfect square?
b. If it is not a perfect square, factor like normal! ﴾Undistributing or unfoiling﴿
4. Does the polynomial contain four or more terms? Try grouping.
5. Is the polynomial completely factored?
Factor:
Check?
This is a list of a student’s final answers on a test. Only one of them is actually finished. Identify which
one is fully factored, then finish factoring the rest of these. You should pay close attention to your test
when you take it. Don't replicate these mistakes!
1.﴿
6.﴿
2.﴿
7.﴿
3.﴿
8.﴿
4.﴿
9.﴿
5.﴿
10.﴿