ALG. 2 CH. 6 POLYNOMALS
PREVIEW
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
____
____
____
____
1. Classify –3x5 – 2x3 by degree and by number of terms.
a. quintic binomial
c. quintic trinomial
b. quartic binomial
d. quartic trinomial
2. Classify –7x5 – 6x4 + 4x3 by degree and by number of terms.
a. quartic trinomial
c. cubic binomial
b. quintic trinomial
d. quadratic binomial
3. Zach wrote the formula w(w – 1)(5w + 4) for the volume of a
rectangular prism he is designing, with width w, which is always has
a positive value greater than 1. Find the product and then classify this
polynomial by degree and by number of terms.
a.
; quintic trinomial
b.
; quadratic monomial
c.
; cubic trinomial
d.
; quartic trinomial
4. Write the polynomial
in standard form.
–6
–2
0
2
6
y
–6
–2
0
2
6
Trees planted (in
thousands)
____
a. quadratic model
c. linear model
b. cubic model
d. none of these
7. Use a graphing calculator to find a polynomial function to model the
data.
x
1
2
3
4
5
6
7
8
9
10
f(x)
12
4
5
13
9
16
19
16
24
43
1.3
18.3
70.5
177.1
357.3
a.
; 630.3 thousand trees
b.
; 630.3 thousand trees
c.
; 618.1 thousand trees
d.
; 618.1 thousand trees
9. The table shows the number of llamas born on llama ranches
worldwide since 1988. Find a cubic function to model the data and
use it to estimate the number of births in 1999.
Years since 1988
a.
c.
b.
d.
2
2
3
5. Write 4x (–2x + 5x ) in standard form. Then classify it by degree and
number of terms.
a. 2x + 9x4; quintic binomial
c. 2x5 – 8x4; quintic trinomial
5
4
b. 20x – 8x ; quintic binomial
d. 20x5 – 10x4; quartic binomial
6. Use a graphing calculator to determine which type of model best fits
the values in the table.
x
____
a. f(x) = 0.8x4 – 1.73x3 + 12.67x2 – 34.68x + 35.58
b. f(x) = 0.08x3 – 1.73x2 + 12.67x + 35.58
c. f(x) = 0.08x4 + 1.73x3 – 12.67x2 + 34.68x – 35.58
d. f(x) = 0.08x4 – 1.73x3 + 12.67x2 – 34.68x + 35.58
8. The table shows the number of hybrid cottonwood trees planted in
tree farms in Oregon since 1995. Find a cubic function to model the
data and use it to estimate the number of cottonwoods planted in
2006.
Years since 1995
1
3
5
7
9
Llamas born (in thousands)
1
3
5
7
9
1.6
20
79.2
203.2
416
a.
; 741,600 llamas
b.
; 563,200 llamas
c.
; 741,600 llamas
d.
; 563,200 llamas
____ 10. Write the expression (x + 6)(x – 4) as a polynomial in standard form.
a. x2 – 10x + 2
c. x2 + 2x – 24
2
b. x + 10x – 24
d. x2 + 10x – 10
____ 11. Write 4x3 + 8x2 – 96x in factored form.
a. 6x(x + 4)(x – 4)
c. 4x(x + 6)(x + 4)
b. 4x(x – 4)(x + 6)
d. –4x(x + 6)(x + 4)
____ 12. Miguel is designing shipping boxes that are rectangular prisms. One
shape of box with height h in feet, has a volume defined by the
function
. Graph the function. What is the
maximum volume for the domain
? Round to the nearest
cubic foot.
a. 10 ft3
b. 107 ft3
c. 105 ft3
d. 110 ft3
____ 13. Use a graphing calculator to find the relative minimum, relative
maximum, and zeros of
. If necessary,
round to the nearest hundredth.
a. relative minimum: (–62.24, 0.36), relative maximum: (37.79, –
3.69),
zeros: x = 5, –2, 2
b. relative minimum: (0.36, –62.24), relative maximum: (–3.69,
37.79),
zeros: x = –5, –2, 2
c. relative minimum: (0.36, –62.24), relative maximum: (–3.69,
37.79),
zeros: x = 5, –2
d. relative minimum: (–62.24, 0.36), relative maximum: (37.79, –
3.69),
zeros: x = –5, –2
____ 14. Find the zeros of
. Then graph the equation.
a 3, 2, –3
c 3, 2
y
y
.
.
–6
b 0, –3, –2
.
–4
6
6
4
4
2
2
–2
2
4
6
x –6
–4
–2
2
–2
–2
–4
–4
–6
–6
d 0, 3, 2
.
y
–6
4
–4
y
6
6
4
4
2
2
–2
2
4
6
x –6
–4
–2
2
–2
–2
–4
–4
–6
–6
4
____ 15. Write a polynomial function in standard form with zeros at 5, –4, and
1.
a.
c.
b.
d.
____ 16. Find the zeros of
and state the multiplicity.
a. 2, multiplicity –3; 5, multiplicity 6
b. –3, multiplicity 2; 6, multiplicity 5
c. –3, multiplicity 2; 5, multiplicity 6
d. 2, multiplicity –3; 6, multiplicity 5
____ 17. Divide
by x + 3.
6
x
a.
c.
b.
, R –93
d.
, R 99
____ 18. Determine which binomial is not a factor of
.
a. x + 4
c. x – 5
b. x + 3
d. 4x + 3
____ 19. Determine which binomial is a factor of
.
a. x + 5
b. x + 20
c. x – 24
d. x – 5
____ 20. The volume of a shipping box in cubic feet can be expressed as the
polynomial
. Each dimension of the box can be
expressed as a linear expression with integer coefficients. Which
expression could represent one of the three dimensions of the box?
a. x + 6
c. 2x + 3
b. x + 1
d. 2x + 1
6
x
Divide using synthetic division.
____ 30. Solve
a. 7
 ,
5
b. no solution
____ 21.
a.
b.
c.
d.
____ 22.
a.
, R 70
c.
b.
, R –62
d.
____ 23. Use synthetic division to find P(2) for
.
a. 2
b. 28
c. 4
, R 46
, R –38
d. –16
Solve the equation by graphing.
____ 24.
a. x = 49
b. no solution
c. x = 19
d. x = 12
____ 25.
a. no solution
b. –2, 0.38
c. 0, 2, –0.38
d. 0, –2, 0.38
____ 26.
a. 3
b. –3
c. –3, 3
d. no solution
____ 27. The dimensions in inches of a shipping box at We Ship 4 You can be
expressed as width x, length x + 5, and height 3x – 1. The volume is
about 7.6 ft3. Find the dimensions of the box in inches. Round to the
nearest inch.
a. 15 in. by 20 in. by 44 in.
c. 15 in. by 20 in. by 45 in.
b. 12 in. by 17 in. by 35 in.
d. 12 in. by 17 in. by 36 in.
Factor the expression.
____ 28.
a.
b.
c.
d.
a.
b.
c.
d.
____ 29.
. Find all complex roots.
c. 7
,
5
d. 7 7
 ,
5 5
ALG. 2 CH. 6 POLYNOMALS
Answer Section
MULTIPLE CHOICE
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A
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B
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A
PREVIEW