Solving Quadratic Equations by Factoring6.66.6

1. Use the zero-factor theorem to solve equations containing expressions in factored form.

2. Solve quadratic equations by factoring.

4. Use the Pythagorean theorem to solve problems.

Factors:

xy 2 factorsx(x + 1) 2 factors(x + 2)(x - 3) 2 factors

What’s the difference?

62 xx 062 xx

Expression: factor Equation: solve

expressions that are multiplied

Quadratic equation in one variable: An equation that can be written in the form

ax2 + bx + c = 0, where a, b, and c are all real numbers and a 0.

Zero-Factor TheoremIf a and b are real numbers and ab = 0,

then a = 0 or b = 0.

04 x0x

035 x 042 xx3x 4or 2 xx

Only works because of the property of 0!Only works because of the property of 0!

Solving Quadratic Equations Using Factoring1. Write in standard form. (Set = 0.)

ax2 + bx + c = 02. Factor.3. Use the zero-factor theorem to solve.

Solve:Solve: 2762 uu

3. Use the zero-factor theorem to solve.

1. Write in standard form. (Set = 0.)

2. Factor.

02762 uu

039 uu

390309

uuuu

3,9

Solve:Solve: 032 pp

3. Use the zero-factor theorem to solve.

1. Write in standard form. (Set = 0.)

2. Factor. 03 pp

3030

ppp

0,3

032 pp

Solve:Solve: 0107 23 xxx

3. Use the zero-factor theorem to solve.

1. Write in standard form. (Set = 0.)

2. Factor.

5205020

xxxxx

0,2,5

0107 23 xxx

01072 xxx 052 xxx

Solve:Solve: kk 716 2

3. Use the zero-factor theorem to solve.

1. Write in standard form. (Set = 0.)

2. Factor.

61

11601016

k

kkkk

1,

61

0176 2 kk

0116 kk

Solve:Solve: 96 mm

3. Use the zero-factor theorem to solve.

1. Write in standard form. (Set = 0.)

2. Factor.

303

mm

3

096

962

2

mm

mm

033 mm

Copyright © 2011 Pearson Education, Inc.

The Pythagorean Theorem Given a right triangle, then a2 + b2 = c2.

c (hypotenuse)

b (leg)

a (leg)

Find the length of the missing side.

a2 + b2 = c2

152 + 362 = c2 Substitute.

225 + 1296 = c2 Simplify exponential forms.

1521 = c2 Add.

c2 – 1521 = 0 Standard form.

(c – 39)(c + 39) = 0 Factor.

c – 39 = 0 or c + 39 = 0

c = 39 or c = –39

Length cannot be negative.

Copyright © 2011 Pearson Education, Inc.

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36

15

Slide 6- 13Copyright © 2011 Pearson Education, Inc.

Solve. x2 = 6x – 8

a) 2 and 4

b) 2 and 4

c) 2 and 4

d) 1 and 8

6.6

Slide 6- 14Copyright © 2011 Pearson Education, Inc.

Solve. x2 = 6x – 8

a) 2 and 4

b) 2 and 4

c) 2 and 4

d) 1 and 8

6.6

Slide 6- 15Copyright © 2011 Pearson Education, Inc.

Find the length of the hypotenuse.

a) 15

b) 46

c) 50

d) 62

?

48

14

6.6

Slide 6- 16Copyright © 2011 Pearson Education, Inc.

Find the length of the hypotenuse.

a) 15

b) 46

c) 50

d) 62

?

48

14

6.6