5­4 Day 1 Factoring 2010
November 23, 2010
5.4 Factoring - Day 1
x2 + bx + c
Objective
Factor trinomials
Dec 6­12:27 PM
1
5­4 Day 1 Factoring 2010
November 23, 2010
Check Skills You'll Need
Simplify each expression:
1. x2 + x + 4x ­ 1
2. 6x2 ­4(3)x + 2x ­ 3
3. 4x2 ­ 2(5 ­ x) ­ 3x
5. (2x ­ 7)(2x ­ 7)
6. 16x2 ­ 9
Multiply:
4. 2x(5 ­ x)
Nov 13­2:20 PM
2
5­4 Day 1 Factoring 2010
November 23, 2010
Factoring is rewriting an expression as the product of its factors. The greatest common factor (GCF) of an expression is a common factor of the terms of the expression.
Nov 13­2:29 PM
3
5­4 Day 1 Factoring 2010
November 23, 2010
Finding Common Factors
Factor each expression:
a. 4x2 + 20x ­ 12 =
b. 9n2 ­ 24n =
Nov 13­2:31 PM
4
5­4 Day 1 Factoring 2010
November 23, 2010
What if there are
no common factors?
Factoring an expression of the form
x2 + bx + c
Nov 13­2:33 PM
5
5­4 Day 1 Factoring 2010
November 23, 2010
Factor x2 + 7x + 12
Step 1: List the factors of 12 (the last number in the trinomial).
Step 2: Which pair of factors adds up to 7 (the second number in the trinomial)?
Step 3: Write the factored form.
x2 + 7x + 12 = (x + 3)(x + 4)
Dec 6­12:36 PM
6
5­4 Day 1 Factoring 2010
November 23, 2010
Factor d2 - 17d + 42
Step 1: List the factors of 42 (the last number in the trinomial).
Step 2: Which pair of factors adds up to ­17 (the second number in the trinomial)?
Step 3: Write the factored form.
d2 ­ 17d + 42 = (d ­ 3)(d ­ 14)
Dec 6­12:45 PM
7
5­4 Day 1 Factoring 2010
November 23, 2010
Factor m2 + 6m - 27
Step 1: List the factors of ­27 (the last number in the trinomial).
Step 2: Which pair of factors adds up to 6 (the second number in the trinomial)?
Step 3: Write the factored form.
m2 + 6m ­ 27 = (m ­ 3)(m + 9)
Dec 6­12:48 PM
8
5­4 Day 1 Factoring 2010
November 23, 2010
Factor x2 - 3x - 28
Step 1: List the factors of ­28 (the last number in the trinomial).
Step 2: Which pair of factors adds up to ­3 (the second number in the trinomial)?
Step 3: Write the factored form.
x2 ­ 3x ­ 28 = (x ­ 7)(x + 4)
Dec 6­12:48 PM
9
5­4 Day 1 Factoring 2010
November 23, 2010
Y
!
Y
R
U
O
OU
N
R
U
T
R
TU
HOMEWORK
RN
!
p. 263 # 1 ­ 24
Dec 6­12:53 PM
10