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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