Page 511 - Algebra 1

Rearranging Before Factoring
Factor completely.
a. -17x+5+12x2
SOLUTION
Before factoring, rearrange the terms so that they are in descending order according to the exponent.
12x2 - 17x + 5
The first term, 12x2, can be factored as (12x)(x), (6x)(2x), and (4x)(3x). The last term, 5, can be factored as (-5)(-1) and (-1)(-5).
Check each pair to see which results in the middle term, -17x.
Example
5
Math Reasoning
Analyze Why are the terms rearranged before factoring?
Possibilities
(12x - 5)(x - 1) (12x - 1)(x - 5) (6x - 5)(2x - 1) (6x - 1)(2x - 5) (4x - 5)(3x - 1) (4x - 1)(3x - 5)
Middle Term
-17x ✓ -61x -16x -32x -19x -23x
So,12x2 -17x+5=(12x-5)(x-1).
b. -2-7x+4x2
SOLUTION
Rearrange the terms in the expression to 4x2 - 7x - 2.
The first term, 4x2, can be factored as (4x)(x) and (2x)(2x).
The last term, -2, can be factored as (-2)(1), (-1)(2), (2)(-1), and (1)(-2).
Check each pair to see which results in the middle term, -7x.
Possibilities
(4x - 2)(x + 1) (4x - 1)(x + 2) (4x + 2)(x - 1) (4x+1)(x-2) (2x - 2)(2x + 1) (2x - 1)(2x + 2) (2x + 2)(2x - 1) (2x + 1)(2x - 2)
Middle Term
2x
7x -2x
-7x ✓ -2x
2x
2x -2x
So,4x2 -7x-2=(4x+1)(x-2).
496 Saxon Algebra 1