Solving
Quadratic
Equations
Solving
Quadratic
Equations
9-6
9-6 by Factoring
by Factoring
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra
Holt
Algebra
11
Solving Quadratic Equations
9-6
by Factoring
Bell Quiz 9-6
Find each product.
2 pts 1.
(x + 2)(x + 7)
2 pts
2. (x – 11)(x + 5)
Factor each polynomial.
2 pts 3.
x2 + 12x + 35
2 pts 5.
x2 – 10x + 16
Holt Algebra 1
2 pts
4. x2 + 2x – 63
10 pts
possible
Solving Quadratic Equations
9-6
by Factoring
Questions on 9-1
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Objective
Solve quadratic equations by factoring.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
A method used to solve quadratic equations is to
factor and use the Zero Product Property.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Example 1A: Use the Zero Product Property
Use the Zero Product Property to solve the
equation. Check your answer.
(x – 7)(x + 2) = 0
Use the Zero Product
Property.
Solve each equation.
Substitute each
solution for x into the
original equation.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Example 1B: Use the Zero Product Property
Use the Zero Product Property to solve each
equation. Check your answer.
(x – 2)(x) = 0
Use the Zero Product
Property.
Solve the second
equation.
Substitute each
solution for x into the
original equation.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Check It Out! Example 1
Use the Zero Product Property to solve each
equation. Check your answer.
1a: (x)(x + 4) = 0
Holt Algebra 1
1b: (x + 4)(x – 3) = 0
Solving Quadratic Equations
9-6
by Factoring
If a quadratic equation is written in standard
form, ax2 + bx + c = 0, then to solve the
equation, you may need to factor before using the
Zero Product Property.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Helpful Hint
To review factoring techniques, see lessons 8-3
through 8-5.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Example 2A: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check
your answer.
x2 – 6x + 8 = 0
Factor the trinomial.
Use the Zero Product
Property.
Solve each equation.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Example 2B: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check
your answer.
x2 + 4x = 21
The equation must be
written in standard
form. So subtract
21 from both sides.
Factor the trinomial.
Use the Zero
Product Property.
Solve each equation.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Example 2C: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check
your answer.
x2 – 12x + 36 = 0
Factor the trinomial.
Use the Zero
Product Property.
Solve each equation.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Example 2D: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check
your answer.
–2x2 = 20x + 50
The equation must be
written in standard
form. So add 2x2 to
both sides.
Factor out the GCF 2.
Factor the trinomial.
Use the Zero Product
Property.
Solve the equation.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Helpful Hint
(x – 3)(x – 3) is a perfect square. Since both
factors are the same, you solve only one of
them.
Holt Algebra 1
Solving Quadratic Equations
9-6
by Factoring
Check It Out! Example 2
Solve the quadratic equation by factoring.
Check your answer.
2a: x2 – 6x + 9 = 0
Holt Algebra 1
2b: x2 + 4x = 5
Solving Quadratic Equations
9-6
by Factoring
Check It Out! Example 2
Solve the quadratic equation by factoring. Check
your answer.
2c: 30x = –9x2 – 25
Holt Algebra 1
2d: 3x2 – 4x + 1 = 0
Solving Quadratic Equations
9-6
by Factoring
Section
9-6 (page 633)
1-6, 9, 11, 15, 18, 20, 21,
23, 25, 26, 28, 29, 41,
44, 49, 61, 62, 65
Holt Algebra 1