April 29, 2015
10-5: Special Factors
Outcome:
• You will learn how to recognize and factor the differences of
squares and perfect square trinomials.
Perfect square trinomials have two equal binomial
factors.
The model below shows the product of (x + 3)2
x
3
x
x2
3x
3
3x
9
*You can also use the FOIL method to find the product.
April 29, 2015
Identifying a Perfect Square Trinomial
1. Is the first term a perfect square?
2. Is the last term a perfect square?
3. Is the middle term twice the product of the square
roots of the first and last term?
Factoring Perfect Square Trinomials
Symbols
Numbers
a2 + 2ab + b2
x2 + 6x + 9 = (x + 3)(x + 3)
a2 - 2ab + b2
x2 - 6x + 9 = (x - 3)(x - 3)
April 29, 2015
Determine whether each trinomial is a perfect square
trinomial. If so, factor it.
1. x2 + 10x + 25
2. 4n2 - 4n + 1
3. 4p2 - 12p + 36
Your Turn ...
a2 + 2a + 1
16x2 + 20x + 25
April 29, 2015
Geometry / Trinomial Connection
The area of a square is x2 + 18x + 81. Find the perimeter.
Step 1: Factor to find measurement of one side
Step 2: Multiply that distance by 4 to get the perimeter.
A polynomial like x2 - 9 is called the difference of squares.
Although this is not a trinomial, it can be factored into two binomials.
x2 - 9 = (x - 3)(x - 3)
April 29, 2015