Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Classify –3x5 – 2x3 by degree
and by number of terms.
a. | quintic binomial | c. | quintic trinomial | b. | quartic binomial | d. | quartic
trinomial |
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2.
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Classify –7x5 – 6x4 +
4x3 by degree and by number of terms.
a. | quartic trinomial | c. | cubic binomial | b. | quintic trinomial | d. | quadratic
binomial |
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3.
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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 |
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4.
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Write the polynomial  in standard form.
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5.
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Write 4x2(–2x2 +
5x3) in standard form. Then classify it by degree and number of terms.
a. | 2x + 9x4; quintic binomial | c. | 2x5 –
8x4; quintic trinomial | b. | 20x5 –
8x4; quintic binomial | d. | 20x5 – 10x4; quartic
binomial |
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6.
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Use a graphing calculator to determine which type of model best fits the values
in the table. a. | quadratic model | c. | linear model | b. | cubic model | d. | none of these |
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7.
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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 | | | | | | | | | | | |
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 |
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8.
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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 | | Trees planted
(in thousands) | 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 |
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9.
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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 | 1 | 3 | 5 | 7 | 9 | | Llamas born (in
thousands) | 1.6 | 20 | 79.2 | 203.2 | 416 | | | | | | |
a. |  ; 741,600 llamas | b. |  ; 563,200
llamas | c. |  ; 741,600 llamas | d. |  ; 563,200
llamas |
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10.
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Write the expression (x + 6)(x – 4) as a polynomial in
standard form.
a. | x2 – 10x + 2 | c. | x2 + 2x
– 24 | b. | x2 + 10x – 24 | d. | x2 + 10x –
10 |
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11.
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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) |
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12.
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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 |
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13.
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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 |
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14.
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Find the zeros of  . Then graph the equation. a. | 3, 2, –3
 | c. | 3, 2
 | b. | 0, –3, –2
 | d. | 0, 3, 2
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15.
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Write a polynomial function in standard form with zeros at 5, –4, and
1.
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16.
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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 |
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17.
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Divide  by x + 3.
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18.
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Determine which binomial is not a factor of  . a. | x + 4 | c. | x – 5 | b. | x + 3 | d. | 4x + 3 |
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19.
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Determine which binomial is a factor of  . a. | x + 5 | b. | x + 20 | c. | x – 24 | d. | x –
5 |
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20.
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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 |
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Divide using synthetic division.
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21.
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22.
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a. |  , R 70 | c. |  , R 46 | b. |  , R
–62 | d. |  , R
–38 |
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23.
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Use synthetic division to find P(2) for  .
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Solve the equation by graphing.
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24.
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a. | x = 49 | b. | no solution | c. | x = 19 | d. | x =
12 |
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25.
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a. | no solution | c. | 0, 2, –0.38 | b. | –2, 0.38 | d. | 0, –2,
0.38 |
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26.
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a. | 3 | b. | –3 | c. | –3, 3 | d. | no
solution |
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27.
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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. |
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28.
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Over two summers, Ray saved $1000 and $600. The polynomial  represents her
savings after three years, where x is the growth factor. (The interest rate r is
x – 1.) What is the interest rate she needs to save $1850 after three years? a. | 9.3% | b. | 1.1% | c. | –269.3% | d. | 0.1% |
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Factor the expression.
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29.
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30.
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31.
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32.
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Solve  . Find all complex roots.
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33.
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Ian designed a child’s tent in the shape of a cube. The volume of the tent
in cubic feet can be modeled by the equation  , where s is the side length. What is
the side length of the tent? a. | 4 feet | b. | 16 feet | c. | 64 feet | d. | 8
feet |
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34.
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Solve  . a. | no solution | c. | 3, –3, 5, –5 | b. | 3,
–5 | d. | 3,
–3 |
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35.
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Use the Rational Root Theorem to list all possible rational roots of the
polynomial equation  . Do not find the actual roots. a. | –4, –2, –1, 1, 2, 4 | c. | 1, 2, 4 | b. | no
roots | d. | –4, –1,
1, 4 |
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36.
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Find the rational roots of  . a. | 2, 6 | b. | –6, –2 | c. | –2, 6 | d. | –6,
2 |
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Find the roots of the polynomial equation.
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37.
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a. | –3 ± 5i, –4 | c. | –3 ± i,
4 | b. | 3 ± 5i, –4 | d. | 3 ± i,
4 |
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38.
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39.
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40.
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A polynomial equation with rational coefficients has the roots  . Find two
additional roots.
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41.
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Find a third-degree polynomial equation with rational coefficients that has
roots –5 and 6 + i.
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42.
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Find a quadratic equation with roots –1 + 4i and –1 –
4i.
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43.
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For the equation  , find the number of complex roots and the possible number of
real roots. a. | 4 complex roots; 0, 2 or 4 real roots | b. | 4 complex roots; 1 or 3 real
roots | c. | 3 complex roots; 1 or 3 real roots | d. | 3 complex roots; 0, 2 or 4 real
roots |
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For the equation, find the number of complex roots, the possible number of
real roots, and the possible rational roots.
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44.
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a. | 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1,
±5 | b. | 7 complex roots; 2, 4, or 6 real roots; possible rational roots: ±1,
±5 | c. | 5 complex roots; 1, 3, or 5 real roots; possible rational roots:  , ±1,
±5 | d. | 5 complex roots; 1, 3, or 5 real roots; possible rational roots: ±1,
±5 |
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45.
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a. | 6 complex roots; 2, 4, or 6 real roots; possible rational roots:  | b. | 6 complex roots; 2, 4, or 6 real roots; possible rational roots:  | c. | 6 complex roots; 0, 2, 4, or 6 real roots; possible rational roots:  | d. | 6 complex roots; 0, 2, 4, or 6 real roots; possible rational roots:  |
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46.
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Find all zeros of  .
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47.
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In how many different orders can you line up 8 cards on a shelf?
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48.
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Verne has 6 math books to line up on a shelf. Jenny has 4 English books to line
up on a shelf. In how many more orders can Verne line up his books than Jenny?
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Evaluate the expression.
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49.
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5!
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50.
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a. | 604,800 | b. | 720 | c. | 120 | d. |  |
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51.
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52.
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53.
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54.
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a. | 14,190 | b. | 4 | c. | 8,555 | d. |  |
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55.
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There are 10 students participating in a spelling bee. In how many ways can the
students who go first and second in the bee be chosen?
a. | 1 way | c. | 3,628,800 ways | b. | 90 ways | d. | 45 ways |
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56.
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The Booster Club sells meals at basketball games. Each meal comes with a choice
of hamburgers, pizza, hot dogs, cheeseburgers, or tacos, and a choice of root beer, lemonade, milk,
coffee, tea, or cola. How many possible meal combinations are there?
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57.
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In how many ways can 3 singers be selected from 5 who came to an
audition?
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58.
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There are 6 people on the ballot for regional judges. Voters can vote for any 4.
Voters can choose to vote for 0¸ 1¸ 2¸ 3¸ or 4 judges. In how many different ways
can a person vote?
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Use Pascal’s Triangle to expand the binomial.
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59.
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60.
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61.
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62.
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A manufacturer of shipping boxes has a box shaped like a cube. The side length
is
5a + 4b. What is the volume of the box in terms of a and b?
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63.
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Use the Binomial Theorem to expand  .
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64.
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Determine the probability of getting four heads when tossing a coin four
times.
a. | 0.5 | b. | 0.375 | c. | 0.25 | d. | 0.0625 |
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65.
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Determine the probability that you will get 3 green lights in a series of 5
lights. Assume red and green are equally likely occurrences.
a. | 31.25% | b. | 62.5% | c. | 10% | d. | 31.25% |
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Short Answer
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66.
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The diagram shows a storage building that consists of a cubic base and a
pyramid-shaped top. a. Write an expression for the cube’s volume. b. Write
an expression for the volume of the pyramid-shaped top. c. Write a polynomial expression to
represent the total volume.
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67.
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The table shows the population of Rockerville over a twenty-five year period.
Let 0 represent 1975. Population of Rockerville Year | Population | 1975 | 336 | 1980 | 350 | 1985 | 359 | 1990 | 366 | 1995 | 373 | 2000 | 395 | | |
a. Find a quadratic model for the
data. b. Find a cubic model for the data. c. Graph
each model. Compare the quadratic model and cubic model to determine which is a better
fit.
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68.
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The volume in cubic feet of a box can be expressed as  , or as the
product of three linear factors with integer coefficients. The width of the box is 2 –
x. a. Factor the polynomial to find linear expressions for the height and the
width. b. Graph the function. Find the x-intercepts. What do they
represent? c. Describe a realistic domain for the function. d. Find the maximum
volume of the box.
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69.
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The volume in cubic feet of a workshop’s storage chest can be expressed as
the product of its three dimensions:  . The depth is x + 1. a. Find linear expressions with integer coefficients for the other
dimensions.
b. If the depth of the chest is 6 feet, what are the other
dimensions?
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70.
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State whether each situation involves a combination or a
permutation.
a. 4 of the 20 radio contest winners selected to try for the grand
prize
b. 5 friends waiting in line at the movies
c. 6 students selected at random
to attend a presentation
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71.
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To raise money, a club is selling 500 raffle tickets. Each ticket has a 5%
chance of winning a prize. K’Lynn buys 6 tickets. To the nearest percent, find the probability
of each outcome.
a. winning exactly 1 time
b. winning exactly 2
times
c. winning exactly 4 times
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Essay
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72.
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A model for the height of a toy rocket shot from a platform is  ,
where x is the time in seconds and y is the height in feet. a. Graph the
function. b. Find the zeros of the function. c. What do the zeros represent? Are
they realistic? d. About how high does the rocket fly before hitting the ground?
Explain.
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73.
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Find the rational roots of  . Explain the process you use and show your
work.
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74.
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Use the first 13 rows of Pascal’s triangle. a. Circle the numbers that are multiples of 3. Notice that the
multiples of 3 form triangular groups. How many multiples of 3 are in the uppermost
group?
b. Color the numbers that are multiples of 5. How many multiples of 5 are in the
uppermost triangular group?
c. Draw a triangle around the numbers that are multiples of 7.
How many multiples of 7 are in the triangular group?
d. Look for a pattern. Use the pattern
to predict the number of multiples of 11 that would form the first triangular group.
e.
Does your pattern work for multiples of 4 or 9? If not, for what kind of numbers does your pattern
seem to work?
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Other
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75.
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What are multiple zeros? Explain how you can tell if a function has multiple
zeros.
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76.
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Use division to prove that x = 3 is a real zero of  .
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77.
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A polynomial equation with rational coefficients has the roots  and  .
Explain how to find two additional roots and name them.
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78.
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Use the list of student council members in the table. A committee must be made
up of two students from grades 9, 10, or 11, and another two students from grade 12. How many
different committees can be made? Explain. Name | Grade | Name | Grade | | W. Alba | 10 | J. Nunez | 9 | | A. Brown | 10 | R. O’Brian | 12 | | C. Dwight | 11 | L. Sanchez | 11 | | E. Farrell | 12 | T. Townsend | 10 | | K. Gonzalez | 9 | W. Velez | 11 | | M. Milano | 10 | J. Watson | 12 | | A. Miles | 9 | O. Xavier | 10 | | | | |
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