Name: _____________________________
Class: _____________ Date: __________
PreAssessment Polynomial Unit
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1 Write the polynomial in standard form. Then name the polynomial based on its degree
and number of terms.
2 – 11x2 – 8x + 6x2
A –5x2 – 8x + 2; quadratic trinomial
B 5x2 – 8x – 2; quadratic trinomial
____
C –6x2 – 8x – 2; cubic polynomial
D 6x2 – 8x + 2; cubic trinomial
2 Write the polynomial in standard form.
4g – g3 + 3g2 – 2
A –2 + 4g + 3g2 – g3
B g3 – 3g2 + 4g – 2
____
3 Determine the degree of the polynomial: 7 m6n5
A 5
____
C 3g3 – g2 + 4g – 2
D –g3 + 3g2 + 4g – 2
B
11
C 6
D 7
4 Match the expression with its name.
6x3 – 9x + 3
A cubic trinomial
B quadratic binomial
C fourth-degree monomial
D not a polynomial
____
5 Write the perimeter of the figure.
A 9x + 7x
____
B
D 14x
C –14x4 – 10x + 10
D 2x4 + 2x + 10
7 Assume f(w)=4w2 – 4w – 8 and g(w)=2w2 + 3w - 6, find f(w) - g(w).
A 2w2 – 7w – 2
B 6w2 – 1w – 14
____
C 14x + 2
4
4
6 Assume f(x) = −7x − 5x + 5 and g(x) = 7x + 5+ 9x, find f(x)+g(x).
A 2x4 + 2x + 8
B –14x4 + 10x + 10
____
11x + 3x + 2
C 2w2 – 1w – 14
D 6w2 + 7w + 2
2
8 Assume f(u) = 2u − 4 and g(u) = u + 2u − 7, find f(u) ⋅g(u).
3
2
A 2u − 8u − 22u + 28
3
2
B 2u + 8u − 22u + 28
3
C 2u − 6u − 28
3
D 2u − 22u + 28
Page 2
____
9 Find the GCF of the terms of the polynomial.
8x6 + 32x3
A x3
____
B
8x3
C 4x3
D 8x6
10 Use the GCF of the terms to factor the polynomial.
23x4 + 46x3
3
A x (23x + 46)
B
3
23x (x + 2)
4
C 23x (x + 2)
ÁÊ 3
2 ˜ˆ
D 23x ÁÁÁÁ x + 2x ˜˜˜˜
ÁË
˜¯
Factor the following polynomials.
____
____
____
11 3x3 + 3x2 + x + 1
A x(3x2 + x + 1)
B (x + 3)(3x2 – 1)
C 3x2(x + 1)
D (x + 1)(3x2 + 1)
12 6g3 + 8g2 – 15g – 20
A (2g2 – 4)(3g + 5)
B (2g2 + 4)(3g – 5)
C (2g2 – 5)(3g + 4)
D (2g2 + 5)(3g – 4)
13 Factor by grouping.
6x4 – 9x3 – 36x2 + 54x
A 3x(x2 – 6)(2x – 3)
B 3x(x2 + 6)(2x + 3)
C 6x(x2 – 6)(2x – 3)
D 6x(x2 + 6)(2x + 3)
Page 3
____
14 Use a graphing calculator to determine which type of model best fits the values in the
table.
x
–6
–2
0
2
6
y
–6
–2
0
2
6
A quadratic model, it has a
C linear model, it has a constant
constant 2nd difference
1st difference
B cubic model, it has a constant 3rd D none of these
difference
____
15 Use a graphing calculator to find the relative minimum, relative maximum, and zeros
of y = 3x 3 + 15x 2 − 12x − 60. If necessary, round to the nearest hundredth.
A relative minimum: (–62.24, 0.36),
zeros: x = 5, –2, 2
B relative minimum: (0.36, –62.24),
zeros: x = –5, –2, 2
C relative minimum: (0.36, –62.24),
zeros: x = 5, –2
D relative minimum: (–62.24, 0.36),
zeros: x = –5, –2
relative maximum: (37.79, –3.69),
relative maximum: (–3.69, 37.79),
relative maximum: (–3.69, 37.79),
relative maximum: (37.79, –3.69),
Page 4
____
16 Find the zeros of y = x(x − 3)(x − 2). Then graph the equation.
A 3, 2, –3
C 3, 2
B
____
0, –3, –2
D 0, 3, 2
17 Write a polynomial function in standard form with zeros at 5, –4, and 1.
A f(x) = x 3 − 2x 2 − 19x − 9
B f(x) = x 3 − 2x 2 − 19x + 20
C f(x) = x 3 − 21x 2 + 60x − 9
D f(x) = x 3 + 20x 2 − 2x − 19
Page 5
Solve the polynomial.
____
18 x 2 + 7x + 19 = 0
A x = 49
____
no solution
B
–20
D x = 12
C 4
D –16
3 2
2 5
20 For which values of m and n will the binomial m n + m n have a positive value?
A m = –2, n = –2
B m = 3, n = –1
____
C x = 19
19 Evaluate the polynomial 6x − y for x = −3 and y = 2.
A 15
____
B
C m = 1, n = –2
D m = –3, n = –5
21 A fireworks company has two types of rockets called Zinger 1 and Zinger 2. The
2
polynomial −16t + 150t gives the height in feet of Zinger 1 at t seconds after launch.
2
The polynomial −16t + 165t gives the height of Zinger 2 at t seconds after launch. If
the rockets are launched at the same time and both explode 6 seconds after launch,
how much higher is Zinger 2 than Zinger 1 when they explode?
A 414 ft
B
990 ft
C 90 ft
Page 6
D 324 ft
____
22 Write a polynomial with zeros at 4, -2, and 1. Then graph the function.
A P(x) = (x − 4)(x + 2)(x − 1)
C P(x) = (x + 4)(x − 2)(x + 1)
P(x) = (x − 4)(x − 2)(x − 1)
D P(x) = (x + 4)(x + 2)(x + 1)
B
Page 7
____
23 The ticket office at Orchestra Center estimates that if it charges x dollars for box seats
2
for a concert, it will sell 50 − x box seats. The function S = 50x − x gives the estimated
income from the sale of box seats. Graph the function, and use the graph to find the
price for box seats that will give the greatest income.
A
C
$50 per box seat
B
$25 per box seat
D
$20 per box seat
____
$50 per box seat
24 Determine the number of real zeros possible for the polynomial,
5
3
2
p(x) = x + 4x − 2x + 10.
A 10 or less
B 1 or more
C five or less
D five or more
Page 8
____
3
25 Using the polynomial, f(x) = −2x + 4x − 8, explain how the degree and leading
coefficient will effect the end behavior.
A Because the degree is odd, the
C Because the degree is odd, the
ends will point in opposite
ends will point in the same
directions, and because the
direction, and because the
leading coefficient is negative
leading coefficient is negative
the graph will increase from right
the graph will increase from right
to left.
to left.
B Because the degree is odd, the
D Because the degree is odd, the
ends will point in opposite
ends will point in the same
directions, and because the
direction, and because the
leading coefficient is negative
leading coefficient is negative
the graph will decrease from
the graph will decrease from
right to left.
right to left.
Page 9
____
3
26 Describe the transformation of the parent function, f(x) = x , to obtain the function
3
g(x) = (x + 4) + 1. Then make a graph of the new function.
A The new graph will be right 4 and C The new graph will be left 4 and
up 1.
up 1.
B
The new graph will be right 4 and D The new graph will be left 4 and
down 1.
down 1.
Page 10
____
4
27 Find the inverse of P(x) = 2(x − 4) − 2. Determine if the inverse is a function.
−1
A P (x) = 4 2x + 2 + 4, yes it is a
function.
B
____
C P
−1
(x) = 4
1
x + 1 + 4, yes it is a
2
function.
−1
−1
1
P (x) = 4 2x + 2 + 4, no it is not a D P (x) = 4 x + 1 + 4, no it is not
2
function.
a function.
28 Determine if the following is a function, then state the domain and range:
3
2
y = x + 2x − 4x + 5.
A Yes, it is a function. Domain:
ÔÏ
Ô¸
{x|x ∈ ℜ}, Range ÔÌ y|y ∈ ℜ Ô˝
Ó
˛
B Yes, it is a function. Domain:
ÏÔ
Ô¸
{x|x ∈ ℜ}, Range ÌÔ y|y ≥ 5 Ô˝
Ó
˛
C No, it is not a function. Domain:
ÔÏ
Ô¸
{x|x ∈ ℜ}, Range ÔÌ y|y ∈ ℜ Ô˝
Ó
˛
D No, it is not a function. Domain:
ÏÔ
Ô¸
{x|x ∈ ℜ}, Range ÌÔ y|y ≥ 5 Ô˝
Ó
˛
Page 11
____
4
2
29 The graph below is a model of the polynomial: y = x − 5x + 4. Is the graph a function?
What is the domain and range of the function?
A Yes, it is a function. Domain:
ÔÏ
Ô¸
{x|x ∈ ℜ} , Range ÌÔ y|y ∈ ℜ Ô˝
Ó
˛
B No, it is not a function. Domain:
ÔÏ
Ô¸
{x|x ∈ ℜ}, Range ÔÌ y|y ≤ 4 Ô˝
Ó
˛
C Yes, it is a function. Domain:
ÏÔ
Ô¸
{x|x ∈ ℜ} , Range ÌÔ y|y ≥ −2.25 Ô˝
Ó
˛
D No, it is not a function. Domain:
ÔÏ
Ô¸
{x|x ∈ ℜ}, Range ÔÌ y|y ≥ −2.25 Ô˝
Ó
˛
Page 12
____
4
2
30 The graph below is a model of the polynomial: y = x − 5x + 4. Is the inverse of this
graph a function? Why?
A Yes, it is a function. It passes the C Yes, it is a function. It passes the
horizontal line test.
vertical line test.
B No, it is not a function. It fails
D No, it is not a function. It fails
the horizontal line test.
the vertical line test.
Page 13