6.Concept Check Identify each equation as linearor quadratic.
(a) (b)
(c) (d)
7.Students often become confused as to how to handle a constant, such as 2 in the equation
How would you explain to someone how to solve this equation and how
to handle the constant 2?
8.Concept Check The number 9 is a double solutionof the equation Why
is this so?
1 x- 922 =0.
2 x 13 x- 42 =0.
x^2 + 2 x- 3 = 2 x^2 - 2 52 x+ 2 = 0
2 x- 5 = 6 x^2 - 5 =- 4
398 CHAPTER 6 Factoring and Applications
9.Concept Check Look at this “solution.”
WHAT WENT WRONG?
Zero-factor property
The solution set is.
10.Concept Check Look at this “solution.”
WHAT WENT WRONG?
or or
The solution set is E3, 0,^45 F.
x=
4
5
x= 3 x= 0 5 x- 4 = 0
3 x 15 x- 42 = 0
E^17 F
x=
1
7
7 x- 1 = 0
x 17 x- 12 = 0
Solve each equation, and check your solutions. See Example 1.
- 1 x- 621 x- 62 = 0 22. 1 y+ 121 y+ 12 = 0
2 x 13 x- 42 = 0 6 y 14 y+ 92 = 0
t 16 t+ 52 = 0 w 14 w+ 12 = 0
12 x+ 1216 x- 12 = 0 13 x+ 22110 x- 12 = 0
12 m- 721 m- 32 = 0 16 x+ 521 x+ 42 = 0
1 x+ 521 x- 22 = 0 1 x- 121 x+ 82 = 0
Solve each equation, and check your solutions. See Examples 2 –7.
- 67.r^4 = 2 r^3 + 15 r^2 68.x^3 = 3 x+ 2 x^2
x^3 +x^2 - 20 x= 0 y^3 - 6 y^2 + 8 y= 0
r^3 - 2 r^2 - 8 r= 0 x^3 - x^2 - 6 x= 0
9 y^3 - 49 y= 0 16 r^3 - 9 r= 0
12 x+ 721 x^2 + 2 x- 32 = 0 1 x+ 1216 x^2 +x- 122 = 0
12 r+ 5213 r^2 - 16 r+ 52 = 0 13 m+ 4216 m^2 +m- 22 = 0
2 y 1 y+ 132 = 136 t 13 t- 202 =- 12
3 z 12 z+ 72 = 12 4 x 12 x+ 32 = 36
10 y^2 =- 5 y x 1 x- 72 =- 10 r 1 r- 52 =- 6
x^2 = 7 x t^2 = 9 t 6 r^2 = 3 r
4 w^2 - 9 = 0 n^2 = 121 x^2 = 400
y^2 - 9 = 0 m^2 - 100 = 0 16 x^2 - 49 = 0
18 x^2 = 12 + 15 x 9 s^2 + 12 s=- 4 36 x^2 + 60 x=- 25
3 x^2 + 5 x- 2 = 0 6 r^2 - r- 2 = 0 12 p^2 = 8 - 10 p
p^2 - 2 p= 3 m^2 + 8 m+ 16 = 0 x^2 - 6 x+ 9 = 0
x^2 = 3 + 2 x x^2 = 4 + 3 x z^2 + 3 z=- 2
r^2 - 4 r+ 3 = 0 x^2 = 24 - 5 x t^2 = 2 t+ 15
y^2 + 3 y+ 2 = 0 p^2 + 8 p+ 7 = 0 y^2 - 3 y+ 2 = 0
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