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5.3 Factoring and Solving Quadratics (work).notebook
October 18, 2016
5.3 FACTORING QUADRATICS
There are several methods available for
solving a quadratic equation:
1.
2.
3.
4.
5.
By Square Roots
By Factoring
By Completing the Square
By the Quadratic Formula
By Graphing
The method depends on the form of the equation.
FACTORING QUADRATIC TRINOMIALS
Example: 5x2 + 17x + 14
1. The expression must be in ascending or
descending order.
2. Make a sum/product chart.
3. Divide each number by the leading coefficient.
4. Reduce each fraction if possible .
5. Denominator = constant or coefficient of first term
Numerator = constant or coefficient of last term
5.3 Factoring and Solving Quadratics (work).notebook
October 18, 2016
Examples:
a. x2 + 6x + 8
b. 3x2 - 11x + 6
Examples:
c. x2 + 7x - 18
d. 3x2 +10x - 8
5.3 Factoring and Solving Quadratics (work).notebook
October 18, 2016
Practice
Factor each trinomial.
1) x2 - 16x + 39
2) x2 + 2x - 35
3) x2 + 22x + 121
4) x2 - 2x - 63
5) 14x2 - 11x + 2
6) 12x2 + 16x - 3
7) 2x2 + 13x + 6
8) 9x2 - 9x - 28
Answers
Factor each trinomial.
1) x2 - 16x + 39
(x - 3)(x - 13)
2) x2 + 2x - 35
(x + 7)(x - 5)
3) x2 + 22x + 121
(x + 11)(x + 11)
4) x2 - 2x - 63
(x + 7)(x - 9)
5) 14x2 - 11x + 2
(7x - 2)(2x - 1)
6) 12x2 + 16x - 3
(2x + 3)(6x - 1)
7) 2x2 + 13x + 6
(2x + 1)(x + 6)
8) 9x2 - 9x - 28
(3x + 4)(3x - 7)
5.3 Factoring and Solving Quadratics (work).notebook
October 18, 2016
Special Factoring Patterns
1. FACTORING DIFFERENCE OF SQUARES
x2 ­ 4 = (x ­ 2)(x + 2)
W
4x ­ 9 = (2x ­ 3)(2x + 3)
2
ha
t
is
th
e
x ­ 49 = (x ­ 7)(x + 7)
2
pa
tt
er
64x2 ­ 25 = (8x ­ 5)(8x + 5)
n?
a2 ­ b2 =
Special Factoring Patterns
2. PERFECT SQUARE TRINOMIALS
x2 + 14x + 49 = (x + 7)2
W
x2 ­ 8x + 16 = (x ­ 4)2
4x2 ­ 20x + 25 = (2x ­ 5)2
9x2 + 12x + 4 = (3x + 2)2
a2 ­ 2ab + b2 =
a2 + 2ab + b2 =
ha
t
is
th
e
pa
tt
er
n
?
5.3 Factoring and Solving Quadratics (work).notebook
October 18, 2016
Practice
Factor completely.
1. 4x 2 - 121
2. 9x 2 - 24x + 16
3. 225 - x 2
4. x 2 + 10x + 25
5. 10x 2 - 13x - 3
Answers
Factor completely.
1. 4x2 - 121
2. 9x 2 - 24x + 16
(2x - 11)(2x + 11)
(3x - 4) 2
3. 225 - x 2
(15 - x)(15 + x)
5. 10x2 - 13x - 3
(2x - 3)(5x + 1)
4. x 2 + 10x + 25
(x + 5)2
5.3 Factoring and Solving Quadratics (work).notebook
October 18, 2016
When factoring,
ALWAYS look for the GCF first!
Greatest Common Factor
the largest factor that divides ALL of the terms
a. 12x2 - 3
b. 7v2 - 42v
FACTOR COMPLETELY
d. 15x2 + 6x
c. 5x2 - 45
e. 3x 2 - 9x + 6
f. 36x - 48x 2 + 24x3
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