Factoring
Polynomials
Section 2.4
Standards Addressed: A1.1.1.5, A1.1.1.5.3, CC.2.2.HS.D.1,
CC.2.2.HS.D.2, CC.2.2.HS.D.5
Essential Questions
 How
does the FOIL method relate to
factoring quadratic trinomials and a
difference of two squares?
 Why should we factor?
Factoring Checklist
 Factor
out the GCF.
 If the polynomial has two or three terms,
look for:


A quadratic trinomial (which can result in a
pair of binomial factors)
A difference of two squares
 Check
that each factor is prime.
 Check your answer by multiplying all of
the factors.
A quadratic trinomial is a trinomial
that is in the format
ax2 + bx + c,
where a, b, and c are integers.
We will only be working with
quadratic trinomials where a = 1.
Factoring a quadratic trinomial
involves recognizing patterns,
estimating, looking for clues, and
multiplying to check.
ax2 + bx + c
Quadratic trinomials can often
be factored as a product of
two binomials. To do so,
determine which two numbers
have a product equal to c
and a sum equal to b.
Example 1: Factor
A.
𝑥 2 + 7𝑥 + 10
Factors of _____ whose sum is _____
B.
𝑚2 − 5𝑚 + 6
Factors of _____ whose sum is _____
Example 1: Factor
C.
𝑦 2 − 5𝑦 − 24
Factors of _____ whose sum is _____
D.
𝑥 2 + 18𝑥 − 63
Factors of _____ whose sum is _____
Worksheet:
Factoring Trinomials
Some binomials can be
factored as a difference of
two squares.
a2 – b2 = (a + b)(a – b)
Example 2: Factor
A.
𝑥2 − 9
B.
4𝑚2 − 25
C.
9𝑥 2 + 81
Always check to make sure
all polynomials are
factored completely.
Example 3: Factor
A.
2𝑘 2 − 50
B.
3𝑦 2 + 45𝑦 − 48
C.
−5𝑑2 − 45𝑑 − 90