Factoring
January 27, 2010
Factoring
x2 + bx + c
Objective
factor trinomials & solve
quadratics by factoring.
Dec 6­12:27 PM
1
Factoring
January 27, 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
Multiply:
4. 2x(5 ­ x)
5. (2x ­ 7)(2x ­ 7)
6. (x + 7)(x ­ 7)
Nov 13­2:20 PM
2
Factoring
January 27, 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
Factoring
January 27, 2010
Finding Common Factors
Factor each expression:
a. 4x2 + 20x ­ 12 =
b. 9n2 ­ 24n =
Nov 13­2:31 PM
4
Factoring
January 27, 2010
What if there are
no common factors?
Factoring an expression of the form
x2 + bx + c
Nov 13­2:33 PM
5
Factoring
January 27, 2010
Factor x2 + 7x + 12
Step 1: List the factors of 12 (the last number in the trinomial).
Step 2: Which pair of factors combines (adds or subtracts) 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
Factoring
January 27, 2010
Factor d2 - 17d + 42
Step 1: List the factors of 42 (the last number in the trinomial).
Step 2: Which pair of factors combines 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
Factoring
January 27, 2010
Factor m2 + 6m - 27
Step 1: List the factors of ­27 (the last number in the trinomial).
Step 2: Which pair of factors combines 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
Factoring
January 27, 2010
Factor x2 - 3x - 28
Step 1: List the factors of ­28 (the last number in the trinomial).
Step 2: Which pair of factors combines 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
Factoring
January 27, 2010
Solve by Factoring
Jan 22­9:02 AM
10
Factoring
January 27, 2010
Solve by Factoring
x2 + 7x + 10 = 0
Step 1: Factor first.
x2 + 7x + 10 = 0
Step 2: Using the zero-product property, solve for x.
Jan 22­9:02 AM
11
Factoring
January 27, 2010
Solve by Factoring
x2 - 3x - 18 = 0
Step 1: Factor first.
x2 - 3x - 18 = 0
Step 2: Using the zero-product property, solve for x.
Jan 22­9:02 AM
12
Factoring
January 27, 2010
Solve by Factoring
x2 + 10x + 21 = 0
Step 1: Factor first.
x2 + 10x + 21 = 0
Step 2: Using the zero-product property, solve for x.
Jan 22­9:02 AM
13
Factoring
January 27, 2010
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HOMEWORK
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factoring worksheet
Dec 6­12:53 PM
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