Download factoring trinomials

Lesson 9.5: Factor x2 + bx + c
Goal: Factor trinomials of the form x2 + bx + c.
In Lesson 9.2, we learned that
(x + 3)(x + 4) = x2 + 4x + 3x + 12 = x2 + 7x + 12
In this lesson, we will reverse this process to factor trinomials of the form x2 + bx + c.
FACTORING TRINOMIALS

The goal in factoring trinomials is to find two numbers that multiply to give you
the back number, but those same two numbers add/subtract to give you the middle
number.
o The following table will be very beneficial to knowing what operations to
put into your parenthesis when factoring based on your problem…
Problem
Factored Answer
+ +
( + )( + )
- +
( - )( - )
+ -
( + )( - ) *largest # goes w/+
- -
( + )( - ) *largest # goes w/-
Examples:
a. x2 + 10x + 16
b. x2 + 3y – 10
Factors of 16:
1 x 16
2x8
4x4
Factors of 10:
1 x 10
2x5

Find the set of factors that will add/subtract to equal the middle number
(x + 2)(x + 8)
(x + 5)(x – 2)
c. x2 – 5x + 6
d. x2 – 7x – 18
Factors of 6:
1x6
2x3
Factors of 18:
1 x 18
2x9
3x6

Find the set of factors that will add/subtract to equal the middle number
(x – 3)(x – 2)
(x + 2)(x – 9)
You Try…
Factor each trinomial.
57. x2 + 7x + 12
58. x2 + 9x + 8
61. z2 + 2z – 24
62. x2 – 11x – 60
59. x2 – 9x + 20
60. y2 + 4y – 21
~This concludes Section 9.5…if you have any
questions over this material, make sure to bring
them to class tomorrow!