5.3 part 3 – Solving

Quadratic Equations by

Factoring

Objective: TSW solve quadratic equations

by factoring.

Answers to Homework 1. (x+6)(x-6) 10. (3x+7)(x-1)

2. (7x-4)(7x+4) 11. (x+5)(2x+3)

3. (5c-b)(5c+b) 12. (3x+4)(3x-2)

4. (2x2 – 9y)(2x2 +9y) 13. (2x-7)(x+2)

5. 3(x-3)(x+3) 14. (4y + 1)(3y + 1)

6. 2(x-1)(x+1) 15. (x+5)(2x-1)

7. (x-1)(7x-4) 16. (2x+3)(x+2)

8. (n+3)(5n+2) 17. (4a-3)(2a-1)

9. (2y+3)(2y+1) 18. (y-4)(2y+5)

To Solve a Quadratic Equation by Factoring:

1. Put the equation in standard form AND

Factor the equation completely.

2. Set each factor equal to zero.

• Zero Product Property – where you can set

each factor equal to zero.

• A factor is ANYTHING with an x in it

3. Solve for x (Which are the values where

the parabola crosses the x-axis)

4. Check Solutions

Examples: Solve each equation by factoring:

1. f(x) = -2x2 + 11x

Let’s factor – GCF is -x, so:

0 = -x(2x – 11)

Each item which has an x is set equal to zero:

-x = 0 2x – 11 = 0

-1 -1 + 11 +11

x = 0 2x = 11

2 2

x = 0, 11

2

2. x2 – 14x = -45

+45 +45

x2 – 14x + 45 = 0

Now let’s factor:

No GCF, so what multiplies to (a·c = 45)

and adds to (b=-14)?

-9 and -5

(x – 9)(x – 5)=0

x – 9 = 0 x – 5 = 0

+9 +9 + 5 +5

x = 9 x = 5

3. h(x) = 25x2 – 16

0 = 25x2 – 16

It’s a difference of two perfect squares:

0 = (5x – 4)(5x + 4)

Set each factor equal to zero.

5x – 4 = 0 5x + 4 = 0

+4 +4 - 4 -4

5x = 4 5x = -4

5 5 5 5

x = 4, -4

5 5

4. g(x) = 3x2 + 12x

GCF is 3x, so:

g(x) = 3x(x + 4)

0 = 3x(x + 4)

Set each factor equal to zero:

3x = 0 x + 4 = 0

3 3 - 4 -4

x = 0 x = -4

x = 0, -4

5. 4x2 + 1 = 4x

Standard form: 4x2 – 4x + 1 = 0

No GCF, so what two numbers multiply to (a·c = 4) and add to (b = -4)?

-2 and -2

(x – 2)(x – 2)

Since a=4, we MUST use Bottom’s Up

(x – 2)(x – 2)

4 4

(x - ½)(x - ½)

(2x – 1)(2x – 1)

2 x – 1 = 0 2x – 1 = 0

+ 1 +1 + 1 +1

2x = 1 2x = 1

2 2 2 2

x = ½ x = ½

6. 5x2 – 5x = 30

5x2 – 5x – 30 = 0

GCF is 5, so:

5(x2 – x – 6)

What multiplies to (a·c = -6) and adds to

(b = -1)?

-3 and 2

5(x – 3)(x + 2) = 0, only items with an x we set equal to zero, so:

x – 3 = 0 x + 2 = 0

+3 +3 - 2 -2

x = 3 x = -2

A parabola is

even found

on this lovely

smiley face

HAVE A NICE TURKEY DAY!

Homework

5.3 part 3 page 272 #’s 13-15, 38-43, 59,60