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Learning Target: I can factor perfect square trinomials and the difference of squares.
Perfect Square Trinomials
A perfect square trinomial is a trinomial whose factors are two identical binomials.
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
Use the following questions to identify whether or not x2 + 18x + 81 is a perfect square trinomial.
Is the first term a perfect square?
Is the last term a perfect square?
Is the middle term twice the product
of the square root of each term?
What is the factored form?
Yes, x2 = x x
Yes, 81 = 9 9
Yes, 18x = 2(x)(9)
Using a2 + 2ab + b2 = (a + b)2
x2 + 18x + 81 = (x + 9)2
Once the trinomial has been identified as a perfect square trinomial, the sign of the middle term will
determine the sign of the binomial.
x2 + 18x + 81 = (x + 9)2
x2 – 18x + 81 = (x – 9)2
Difference of Two Squares
The difference of two squares can be factored as the product of the sum and difference of two
binomials.
a2 – b2 = (a – b)(a + b)
Use the following questions to factor 4x2 – 121.
Is the first term a perfect square?
Yes, 4x2 = 2x 2x
Is the last term a perfect square?
Yes, 121 = 11 11
What is the factored form?
Using a2 – b2 = (a + b)(a – b), the
factored form is:
4x2 – 121 = (2x + 11)(2x -11)
Factoring completely
When
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completely factoring polynomials
Always factor out a GCF
For a binomial, determine if it is the difference of two squares
For a trinomial, determine if it is a factorable trinomial or a perfect square trinomial
For a polynomial with 4 terms, factor by grouping
Factor 4x2 – 100
There are two ways to factor 4x2 – 100
#1: Factor the difference of two squares first.
#2: Factor out GCF first.
2
4x – 100
4x2 – 100
(2x + 10)(2x – 10)
4(x2 – 25)
(2)(x + 5)(2)(x – 5)
4(x + 5)(x – 5)
4(x + 5)(x – 5)