### 5.3 – Solving Quadratic Equations by Factoring

Inequalities
Chapter 5 – Quadratic Functions and Inequalities
5.3 – Solving Quadratic Equations by Factoring
Equations by Factoring
 In this section we will learn how to:
 Write quadratic equations in intercept form
 Solve quadratic equations by factoring
Equations by Factoring
 Intercept form – of a quadratic equation is
 y = a(x – p)(x – q)
 p and q represent the x-intercepts of the graph
corresponding to the equation
Equations by Factoring
 Changing a quadratic in intercept form to standard
forms requires using the FOIL method
 First
 Outer
 Inner
 Last
 Multiply the terms: first, outer, inner, last
 Combine any like terms
Equations by Factoring
 Example 1
 (6x + 1)(2x – 4)
Equations by Factoring
 Example 2
 (-3x + 5)(3x + 2)
Equations by Factoring
 Example 3
 (9x – 2)2
Equations by Factoring
 Example 4
 (6x + 3)2
Equations by Factoring
 Example 5
 (x + 7)3
Equations by Factoring
 Example 6
 (2x + 4)3
Equations by Factoring
 Example 7
 (3x – 1)3
Equations by Factoring
HOMEWORK
5.3 Part 1 Worksheet
Equations by Factoring
 Find the Greatest Common Factor (GCF)
 If all the terms of a polynomial have a factor(s) in
common, you can factor out that greatest common factor
Equations by Factoring
 Example 1
 Factor out the GCF
 8y2 + 16y5 =
 6a4 – 8a2 + 2a =
 -15x3y + 9x2y7 =
 -5x2y – x2 + 3x3y5 + 11x7 =
Equations by Factoring
CLASSWORK
5.3 Part 2 Practice
Equations by Factoring
 Factoring a Difference of Perfect Squares
 If you have a quadratic equation that has the difference of
two terms that are both perfect squares, it factors as:
 A2 – B2 = (A + B)(A – B)
Equations by Factoring
 Example 1
 Factor:
 x2 – 9 =
 4x2 – 25 =
 9x2 – 16y2 =
Equations by Factoring
 Example 2
 Factor:
 100x2 – 81y2 =
 3x2 – 75 =
 20x2 – 5y2 =
Equations by Factoring
CLASSWORK/HOMEWORK
Equations by Factoring
 Factoring a Trinomial
 Ax2 ± Bx + C =
 ADD inner and outer to get B
 ( + )( + )
 ( - )( - )
Equations by Factoring
 Example 1
 Factor:
 x2 + 10x + 9
 x2 + 8x + 15
 x2 – 10x + 25
Equations by Factoring
 Example 2
 Factor:
 x2 – 2x + 1
 x2 – 14x + 24
 x2 + 6x + 9
Equations by Factoring
HOMEWORK
5.3 Part 3 Practice
Equations by Factoring
 Factoring a Trinomial
 Ax2 ± Bx - C =
 SUBTRACT inner and outer to get B
 ( + )( - )
 ( - )( + )
Equations by Factoring
 Example 1
 Factor:
 x2 – 3x – 18
 x2 + 5x – 6
 x2 – 2x – 35
Equations by Factoring
 Example 2
 Factor:
 x2 + 4x – 21
 x2 + x – 20
 x2 – 4x – 5
Equations by Factoring
HOMEWORK
5.3 Part 4 Worksheet
Equations by Factoring
 Factoring a Trinomial
 Ax2 ± Bx + C
 ( + )( + )
 ( - )( - )
 Ax2 ± Bx – C
 ( + )( - )
 ( - )( + )
Equations by Factoring
 Example 1
 Factor:
 2x2 + 3x + 1
 5x2 – 28x – 12
Equations by Factoring
 Example 2
 Factor:
 4x2 – 12x + 5
 3x2 + 2x – 16
Equations by Factoring
 Example 3
 Factor:
 4x2 – 14x + 10
 15x2 + 18x – 24
Equations by Factoring
 Example 4
 Factor:
 25x2 – 10x – 3
 3x2 + 11x + 6
Equations by Factoring
HOMEWORK
5.3 Part 5 Worksheet
Equations by Factoring
CLASSWORK
Equations by Factoring
 Solving by Factoring
 If the equation is not equal to zero, rewrite so that it is
 Factor out a GCF if possible
 You now have one of the following:
 A trinomial that must be factored (x2 + Bx + C)
 A difference of two squares that must be factored
(x2 –
C)
 Two expressions
 Set each of the remaining expressions equal to zero and
solve
Equations by Factoring
 Example 1
 Factor and solve:
 x2 + 13x + 30 = 0
 x2 + 5x – 24 = 0
Equations by Factoring
 Example 2
 Factor and solve:
 x2 – 13x = -22
 x2 – 2x = 48
Equations by Factoring
 Example 3
 Factor and solve:
 x2 – 100 = 0
 2x2 – 72 = 0
Equations by Factoring
 Example 4
 Factor and solve:
 x2 + 15x = 0
 2x2 – 6x = 0