Name: ________________________ Class: ___________________ Date: __________
ID: A
Solving Polynomials Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Solve by factoring.
4x 2 + 28x − 32 = 0
1
a. 8, −
2
b.
–8, 4
c.
–8, 1
c.
3
d.
− 3,
c.
6 6
− ,
7 7
d.
1, −
d.
−
1
2
Solve the equation by finding square roots.
____
2. 2x 2 = 6
a.
b.
____
− 6
2
3, –
6
,
2
3
3. 108x 2 = 147
49 49
a. − ,
36 36
b.
7 7
− ,
6 6
6
36 36
,
49 49
____
4. The function y = −16t 2 + 486 models the height y in feet of a stone t seconds after it is dropped from the
edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a
second.
a. 7.79 seconds
c. 0.25 seconds
b. 11.02 seconds
d. 5.51 seconds
____
5. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the length of the shorter base
to be 3 yards greater than the height, and the length of the longer base to be 5 yards greater than the height.
For what height will the garden have an area of 360 square yards? Round to the nearest tenth of a yard.
a. 17.1 yards
c. 39.2 yards
b. 34.2 yards
d. 152.6 yards
Solve the equation.
____
____
6. x 2 + 18x + 81 = 25
a. 14, 4
b. –4, –14
c.
d.
7. Find the missing value to complete the square.
x 2 + 2x + ____
a. 2
b. 1
c.
1
14, –14
–4, 4
4
d.
8
Name: ________________________
ID: A
Solve the quadratic equation by completing the square.
____
____
8. x 2 + 10x + 14 = 0
a. −10 ± 6
b. 100 ± 11
c.
d.
5 ±6
−5 ±
9. x 2 + 10x + 35 = 0
a. −10 ± 15
c.
100 ± i 10
−5 ± i 10
b.
5 ± i 15
d.
11
____ 10. −3x 2 + 7x = −5
a.
7
±
6
b.
7
− ±
3
109
6
109
3
67
3
c.
7
±
3
d.
7
− ±
6
22
6
c.
7
− ±
6
59
i
6
d.
7
±
3
____ 11. 3x 2 + 7x = −9
a.
7
±
6
b.
7
− ±
3
20
i
6
101
i
3
59
i
3
Rewrite the equation in vertex form.
____ 12. y = x 2 + 10x + 16
a.
b.
y = (x + 5) 2 + 41
y = (x + 10) 2 − 9
c.
d.
y = (x + 10) 2 + 11
y = (x + 5) 2 − 9
Use the Quadratic Formula to solve the equation.
____ 13. 5x 2 + 9x − 2 = 0
2
a.
, −4
5
b.
1
, −2
5
c.
2
56
, −13
5
d.
2, −
1
5
Name: ________________________
ID: A
____ 14. −2x 2 + x + 8 = 0
a.
1
±
4
65
4
c.
1
±
2
65
2
b.
4±
130
4
d.
1
±
4
32
2
____ 15. 4x 2 − x + 3 = 0
a.
1
±
8
47
8
c.
1 i 47
±
8
8
b.
8±
i 94
8
d.
1 i 47
±
4
4
____ 16. Write a polynomial function in standard form with zeros at 5, –4, and 1.
a. f(x) = x 3 − 21x 2 + 60x − 9
c. f(x) = x 3 − 2x 2 − 19x − 9
3
2
b. f(x) = x − 2x − 19x + 20
d. f(x) = x 3 + 20x 2 − 2x − 19
Factor the expression.
____ 17. x 4 − 20x 2 + 64
a. (x − 2)(x − 2)(x + 4)(x + 4)
b. (x − 2)(x − 4)(x 2 )
c.
d.
3
(x − 2)(x + 2)(x − 4)(x + 4)
no solution