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5.4 Factoring Quadratic Expressions

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5.4 Factoring Quadratic Expressions Golden Rules of Factoring Example: Factor out the greatest common factor 4x2 + 20x -12 Practice: Factor each expression a) 9x2 ... – PowerPoint PPT presentation

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Title: 5.4 Factoring Quadratic Expressions


1
5.4 Factoring Quadratic Expressions
2
WAYS 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

3
By Graphing
y (x 2)(x 4)
By looking at the roots, we can get the
solutions. Here, the solutions are -2 and 4.
4
Golden Rules of Factoring
5
Example Factor out the greatest common factor
  • 4x2 20x -12

6
Practice 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

7
Factor Diamonds
x² 8x 7 0
7
1
7
8
(x 1) (x 7) 0
So your answers are -1 and -7
8
Practice Solve by a factor diamond
  • X2 15x 36

(x3)(x12)
9
Bottoms 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
10
Practice Solve using Bottoms
Up/Barrowing Method
  • 2x2 19x 24

(x-8)(2x-3)
11
Factor 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
12
Practice Factor by Grouping
  • 3x2 7x - 20

(x4)(3x-5)
13
SHORTCUTS
  • a2 2ab b2 (ab)2

Example 25x2 90x 81
(5x 9)2
  • a2 - 2ab b2 (a - b)2

Example 9x2 42x 49
(3x 7)2
  • a2 - b2 (ab)(a - b)

Example x2 64
(x 8)(x 8)
14
Practice Problems Solve using any method
  • Solutions
  • a) (x-6)(3x2)
  • (x2)(4x-3)
  • (2x7)(2x-7)
  • (x4)(2x3)
  1. 3x2 16x 12
  2. 4x2 5x 6
  3. 4x2 49
  4. 2x2 11X 12
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