Objective: By the end of class, I will be able to…
Example 1: Review—Multiply each pair of polynomials
A. 5𝑥(𝑥 + 2)
B. (𝑥 − 2)(𝑥 − 9)
C. (𝑥 + 5)(𝑥 − 6)
Example 2: Review Greatest Common Factor—factor out the greatest common factor of each polynomial
A. 3𝑥 2 + 9𝑥
B. −5𝑥 + 15
C. 2𝑥 2 − 4𝑥 + 8
D. −12𝑥 5 + 24𝑥 2
E. 5𝑥 2 − 10𝑥 + 12
F. −3𝑥 3 + 9𝑥 2 − 12𝑥
G. 4𝑥 + 12
H. −𝑥 − 7
I. 5𝑥 2 − 10𝑥 + 5
An Introduction to Factoring
Example 3: Let’s Play a Game
A. Two numbers multiply to 15 and add to 8. What are they?
B. Two numbers multiply to 20 and add to 12. What are they?
C. Two numbers multiply to -32 and add to 4. What are they?
D. Two numbers multiply to 27 and add to -12. What are they?
Example 4: Graph 𝑓(𝑥) = 𝑥 2 + 7𝑥 + 10 on your calculator.
What are the zeros of the parabola?
What do 𝑟1 and 𝑟2 multiply to?
𝑦 = (𝑥 − 𝑟1 )(𝑥 − 𝑟2 )
Write the equation in factored form:
What do 𝑟1 and 𝑟2 add to?
Example 5: Graph 𝑔(𝑥) = 𝑥 2 + 3𝑥 − 10 on your calculator.
What are the zeros of the parabola?
What do 𝑟1 and 𝑟2 multiply to?
𝑦 = (𝑥 − 𝑟1 )(𝑥 − 𝑟2 )
Write the equation in factored form:
What do 𝑟1 and 𝑟2 add to?
Using a Multiplication Table
Example 6: Use the multiplication table to find the product of (𝑥 + 1) and (𝑥 + 6).
(𝑥 + 1)(𝑥 + 6) =
Example 7: Go Backwards! Use the multiplication table to write 𝑥 2 + 5𝑥 + 4 as the product of two
binomials.
Factors of 4
Example 8: Factor each of the following using a multiplication table.
A. 𝑥 2 − 6𝑥 + 9
B. 𝑥 2 + 5𝑥 − 6
C. 𝑥 2 + 9𝑥 + 20
D. 𝑥 2 − 10𝑥 − 24
Without the Table
Example 9: Write ℎ(𝑥) = 𝑥 2 + 7𝑥 − 18 in factored form, i.e. factor 𝑥 2 + 7𝑥 − 18
What multiplies to ____________ and adds to ___________?
Answer: _______ and _______
Factored Form:
Example 10: Factor 𝑥 2 + 12𝑥 + 27
What multiplies to ________ and adds to __________?
Answer: ______ and ______
Factored Form:
Example 11: Factor each of the following expressions
A. 𝑥 2 + 5𝑥 − 24
B. 𝑥 2 − 3𝑥 − 28
C. 𝑥 2 − 13𝑥 + 36
D. 𝑥 2 − 4𝑥 − 32
E. 𝑥 2 − 15𝑥 + 36
F. 𝑥 2 + 21𝑥 + 54
Including a Greatest Common Factor
Example 12: Completely factor each expression. Factor out a greatest common factor, then factor the
remaining trinomial.
A. 2𝑥 2 + 8𝑥 + 6
B. 2𝑥 2 + 12𝑥 − 80
C. 4𝑥 2 − 20𝑥 + 16
D. −2𝑥 2 + 4𝑥 + 30