Download Lesson 8_2

Warm-Up
Lesson 8.2: Solving Equations by
Factoring ax2 + bx + c when a ≠ 1
Given ax2 + bx + c where a ≠ 1, apply the following
strategy to try to factor:
1. Find two numbers where the product is
a  c and the sum is b.
2. Use these numbers to expand bx and then
factor by grouping?
Example
Factor 2 x 2  11x  5
Find two numbers where the product is
a  c  2  5  10 and the sum is 11.
The two numbers are 10 and 1, so
expand 11x into 10x + 1x and then factor
by grouping. 2 x 2  10 x  1x  5
2 x( x  5)  1( x  5)
( x  5)(2 x  1)
Therefore, 2x 2  11x  5  ( x  5)(2 x  1)
Example
Factor 8 x 2  13 x  6
Find two numbers where the product is
a  c  8  (6)  48 and the sum is 13.
The two numbers are 16 and -3, so
expand 13x into 16x - 3x and then factor
by grouping. 8 x 2  16 x  3 x  6
8 x( x  2)  3( x  2)
( x  2)(8 x  3)
Therefore, 8x 2  13 x  6  ( x  2)(8 x  3)
Example
2
2
2x
+
7x
2
=
4x
+4
solve
First set equal to zero: 2 x 2  7 x  6  0
Now find two numbers where the product is
12 and the sum is -7: 3 and  4
Expand -7x into -4x - 3x and then factor by
2
grouping.
2 x  4 x  3x  6
2 x( x  2)  3( x  2)
( x  2)(2 x  3)
Therefore, the solutions are x  2 and x 
3
2
Your Turn
Solve the following equations.
1. 3 x 2  20 x  12  0
( x  6)(3 x  2)  0
x  6 and x 
2
3
2
4
x
 2 x  30  0
2.
2(2 x  x  15)  0
2
2( x  3)(2 x  5)  0
x  3 and x 
5
2