5.4 Factoring Quadratic Expressions

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5.4 Factoring Quadratic Expressions
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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

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

• 4x2 20x -12

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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

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

• X2 15x 36

(x3)(x12)
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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
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Practice Solve using Bottoms
Up/Barrowing Method

• 2x2 19x 24

(x-8)(2x-3)
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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
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Practice Factor by Grouping

• 3x2 7x - 20

(x4)(3x-5)
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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)
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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