Title: 5.4 Factoring Quadratic Expressions
15.4 Factoring Quadratic Expressions
2WAYS TO SOLVE A QUADRATIC EQUATION ax² bx c
0
- There are many ways to solve a quadratic.
- The main ones are
- Graphing
- Factoring
- Bottoms Up
- Grouping
- Quadratic formula
- Completing the square
3By Graphing
y (x 2)(x 4)
By looking at the roots, we can get the
solutions. Here, the solutions are -2 and 4.
4Golden Rules of Factoring
5Example Factor out the greatest common factor
6Practice Factor each expression
- Solutions
- a.) 3(3x2 x 6)
- b) 7(p2 3)
- c) 2w(2w 1)
- a) 9x2 3x 18
- b) 7p2 21
- c) 4w2 2w
7Factor Diamonds
x² 8x 7 0
7
1
7
8
(x 1) (x 7) 0
So your answers are -1 and -7
8Practice Solve by a factor diamond
(x3)(x12)
9Bottoms up (Borrowing Method)
2x² 13x 6 0
x² 13x 12 0
12
1
12
(x 12) (x 1) 0
13
2
2
(x 6) (x 1) 0 2
Multiply by 2 to get rid of the fraction
(x 6) (2x 1) 0
So your answers are -6 and -1/2
10Practice Solve using Bottoms
Up/Barrowing Method
(x-8)(2x-3)
11Factor by Grouping
2x² 7x 15 0
2x² 10x 3x 15 0
-30
3
-10
-7
Note you are on the right track because you have
(x-5) in both parenthesis
2x(x 5) 3(x 5) 0
(2x 3)(x 5)0
So your answers are -3/2 and 5
12Practice Factor by Grouping
(x4)(3x-5)
13SHORTCUTS
Example 25x2 90x 81
(5x 9)2
Example 9x2 42x 49
(3x 7)2
Example x2 64
(x 8)(x 8)
14Practice Problems Solve using any method
- Solutions
- a) (x-6)(3x2)
- (x2)(4x-3)
- (2x7)(2x-7)
- (x4)(2x3)
- 3x2 16x 12
- 4x2 5x 6
- 4x2 49
- 2x2 11X 12