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 C –6x2 – 8x – 2; cubic polynomialB 5x2 – 8x – 2; quadratic trinomial D 6x2 – 8x + 2; cubic trinomial

____ 2 Write the polynomial in standard form.

4g – g3 + 3g2 – 2

A –2 + 4g + 3g2 – g3 C 3g3 – g2 + 4g – 2B g3 – 3g2 + 4g – 2 D –g3 + 3g2 + 4g – 2

____ 3 Determine the degree of the polynomial: 7m6n5

A 5 B 11 C 6 D 7

____ 4 Match the expression with its name.

6x3 – 9x + 3

A cubic trinomial C fourth-degree monomialB quadratic binomial D not a polynomial

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____ 5 Write the perimeter of the figure.

A 9x + 7x B 11x + 3x + 2 C 14x + 2 D 14x

____ 6 Assume f(x) = −7x−5x4

+5 and g(x) = 7x4

+5+9x, find f(x)+g(x).

A 2x4 + 2x + 8 C –14x4 – 10x + 10B –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 C 2w2 – 1w – 14

B 6w2 – 1w – 14 D 6w2 + 7w + 2

____ 8 Assume f(u) = 2u−4 and g(u) = u2

+2u−7, find f(u) ⋅g(u).

A 2u3

−8u2

−22u+28 C 2u3

−6u−28

B 2u3

+8u2

−22u+28 D 2u3

−22u+28

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____ 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

A x323x+46( ) B 23x

3x+2( ) C 23x

4(x+2) D 23x x

3+2x

2Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

Factor the following polynomials.

____ 11 3x3 + 3x2 + x + 1

A x(3x2 + x + 1) C 3x2(x + 1)

B (x + 3)(3x2 – 1) D (x + 1)(3x2 + 1)

____ 12 6g3 + 8g2 – 15g – 20A (2g2 – 4)(3g + 5) C (2g2 – 5)(3g + 4)

B (2g2 + 4)(3g – 5) D (2g2 + 5)(3g – 4)

____ 13 Factor by grouping.

6x4 – 9x3 – 36x2 + 54x

A 3x(x2 – 6)(2x – 3) C 6x(x2 – 6)(2x – 3)

B 3x(x2 + 6)(2x + 3) D 6x(x2 + 6)(2x + 3)

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____ 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 constant 2nd difference

C linear model, it has a constant 1st difference

B cubic model, it has a constant 3rd difference

D none of these

____ 15 Use a graphing calculator to find the relative minimum, relative maximum, and zeros

of y = 3x3 + 15x2 − 12x − 60. 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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____ 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) = x3 − 2x2 − 19x − 9 C f(x) = x3 − 21x2 + 60x − 9

B f(x) = x3 − 2x2 − 19x + 20 D f(x) = x3 + 20x2 − 2x − 19

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Solve the polynomial.

____ 18 x2 + 7x + 19 = 0

A x = 49 B no solution C x = 19 D x = 12

____ 19 Evaluate the polynomial 6x − y for x = −3 and y = 2.

A 15 B –20 C 4 D –16

____ 20 For which values of m and n will the binomial m3n2

+ m2n5 have a positive value?

A m = –2, n = –2 C m = 1, n = –2B m = 3, n = –1 D m = –3, n = –5

____ 21 A fireworks company has two types of rockets called Zinger 1 and Zinger 2. The

polynomial −16t2

+ 150t gives the height in feet of Zinger 1 at t seconds after launch.

The polynomial −16t2

+ 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 D 324 ft

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____ 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)

B P(x) = (x−4)(x−2)(x−1) D P(x) = (x+4)(x+2)(x+1)

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____ 23 The ticket office at Orchestra Center estimates that if it charges x dollars for box seats

for a concert, it will sell 50 − x box seats. The function S = 50x − x2 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

$50 per box seat

C

$25 per box seatB

$20 per box seat

D

$50 per box seat

____ 24 Determine the number of real zeros possible for the polynomial,

p(x) = x5

+4x3

−2x2

+10.

A 10 or less C five or lessB 1 or more D five or more

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____ 25 Using the polynomial, f(x) = −2x3

+4x−8, explain how the degree and leading

coefficient will effect the end behavior.

A Because the degree is odd, the ends will point in opposite directions, and because the leading coefficient is negative the graph will increase from right to left.

C Because the degree is odd, the ends will point in the same direction, and because the leading coefficient is negative the graph will increase from right to left.

B Because the degree is odd, the ends will point in opposite directions, and because the leading coefficient is negative the graph will decrease from right to left.

D Because the degree is odd, the ends will point in the same direction, and because the leading coefficient is negative the graph will decrease from right to left.

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____ 26 Describe the transformation of the parent function, f(x) = x3, to obtain the function

g(x) = (x+4)3

+1. Then make a graph of the new function.

A The new graph will be right 4 and up 1.

C The new graph will be left 4 and up 1.

B The new graph will be right 4 and down 1.

D The new graph will be left 4 and down 1.

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____ 27 Find the inverse of P(x) = 2(x−4)4

−2. Determine if the inverse is a function.

A P−1

(x) = 2x+24+4, yes it is a

function.

C P−1

(x) =1

2x+14 +4, yes it is a

function.

B P−1

(x) = 2x+24+4, no it is not a

function.

D P−1

(x) =1

2x+14 +4, no it is not

a function.

____ 28 Determine if the following is a function, then state the domain and range:

y = x3

+2x2

−4x+5.

A Yes, it is a function. Domain:

x|x ∈ ℜ{ }, Range y|y ∈ ℜÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

C No, it is not a function. Domain:

x|x ∈ ℜ{ }, Range y|y ∈ ℜÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

B Yes, it is a function. Domain:

x|x ∈ ℜ{ }, Range y|y ≥ 5ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

D No, it is not a function. Domain:

x|x ∈ ℜ{ }, Range y|y ≥ 5ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

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____ 29 The graph below is a model of the polynomial: y = x4

−5x2

+4. Is the graph a function?

What is the domain and range of the function?

A Yes, it is a function. Domain:

x|x ∈ ℜ{ }, Range y|y ∈ ℜÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

C Yes, it is a function. Domain:

x|x ∈ ℜ{ }, Range y|y ≥ −2.25ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

B No, it is not a function. Domain:

x|x ∈ ℜ{ }, Range y|y ≤ 4ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

D No, it is not a function. Domain:

x|x ∈ ℜ{ }, Range y|y ≥ −2.25ÏÌÓÔÔÔÔ

¸˝˛ÔÔÔÔ

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____ 30 The graph below is a model of the polynomial: y = x4

−5x2

+4. Is the inverse of this

graph a function? Why?

A Yes, it is a function. It passes the horizontal line test.

C Yes, it is a function. It passes the vertical line test.

B No, it is not a function. It fails the horizontal line test.

D No, it is not a function. It fails the vertical line test.