Answers 2627 ALGEBRA II AMixed Degree Systems

Mixed Degree Systems — Unit test Answers

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One root of a third degree polynomial function f(x) is –5 + 2i. Which statement describes the number and nature of all roots for this function?

f(x) has two real roots and one imaginary root.

f(x) has two imaginary roots and one real root.

f(x) has three imaginary roots.

f(x) has three real roots.

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Which of the following is the complete list of roots for the polynomial function ?

–5, 3

–5, 3, –4 + i, –4 – i

–5, 3, –4 + i, 4 + i

–4 + i, –4 – i

Which statement about 4x2 + 19x – 5 is true?

One of the factors is (x – 4).

One of the factors is (4x + 1).

One of the factors is (4x – 5).

One of the factors is (x + 5).

If f(–5) = 0, what are all the factors of the function ? Use the Remainder Theorem.

(x – 2)(x + 5)(x – 3)

(x + 2)(x – 5)(x + 3)

(x – 2)(x + 5)

(x + 2)(x – 5)

What are the solutions of the equation x4 – 5x2 – 36 = 0? Use factoring to solve.

x = ±2 and x = ±3

x = ±2i and x = ±3

x = ±2 and x = ±3i

x = ±2i and x = ±3i

Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands. At their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers. If the prices are the same at both concession stands, what is the price of a hot dog?

$0.40

$2.50

$3.75

$4.00

Which second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?

f(x) = 3x2 + 5x + 4

f(x) = 3x2 + 15x + 12

f(x) = 3x2 – 5x + 4

f(x) = 3x2 – 15x + 12

What is the completely factored form of ?

(2x - 5)(3x + 1)

(2x + 5)(3x - 1)

(2x - 1)(3x - 5)

(2x + 1)(3x + 5)

If (x + k) is a factor of f(x), which of the following must be true?

f(k) = 0

f(–k) = 0

A root of f(x) is x = k.

A y intercept of f(x) is x = –k.

Which polynomial function has x-intercepts –1, 0, and 2 and passes through the point (1, –6)?

f(x) = x3 – x2 – 2x

f(x) = 3x3 – 3x2 – 6x

f(x) = x3 + x2 – 2x

f(x) = 3x3 + 3x2 – 6x

Which second degree polynomial function has a leading coefficient of 2 and roots –3 and 5?

f(x) = 2x2 + 4x – 30

f(x) = 2x2 + 2x – 15

f(x) = 2x2 – 4x – 30

f(x) = 2x2 – 2x – 15

Which statement about the polynomial function g(x) is true?

If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.

If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.

If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.

If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.

Which statement describes the graph of this polynomial function?

The graph crosses the x-axis at x = 2 and x = –1 and touches the x-axis at x = 0.

The graph touches the x-axis at x = 2 and x = –1 and crosses the x-axis at x = 0.

The graph crosses the x-axis at x = –2 and x = 1 and touches the x-axis at x = 0.

The graph touches the x-axis at x = –2 and x = 1 and crosses the x-axis at x = 0.

Which is a factor of f(x) = 60x4 + 86x3 – 46x2 – 43x + 8? Use the Rational Root Theorem to help you find your answer.

x – 6

5x – 8

6x – 1

8x + 5

Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Sharon jumps, Megan throws a beach ball up to Sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?

0.65 seconds

0.92 seconds

1.08 seconds

1.15 seconds

During a pumpkin launching contest, two pumpkins are launched at the same time. The path of pumpkin A is modeled by the equation y = –0.01x2 + 0.32x + 4. The path of pumpkin B is modeled by the equation y = –0.01x2 + 0.18x + 5. If x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent?

the height at which the pumpkins reach their greatest horizontal distance from the launch site

the horizontal distance of the pumpkins from the launch site when they reach the ground

the starting height of the pumpkins when they are at the launch site

the horizontal distance of the pumpkins from the launch site when their heights are the same

A company plans to sell embroidered hats for $15 each. The company’s financial planner estimates that the cost, y, of manufacturing the hats is a quadratic function with a y-intercept of 7,920 and a vertex of (150, 9,000). What is the minimum number of hats the company must sell to make a profit?

151

401

529

601

A store owner puts in an order for product X and product Y for a total of 4,000 units. It costs $0.10 per item to ship of product X and $0.04 per item to ship product Y. If the total shipping cost is $352, which system of equations can be used to determine how much of product X and product Y the store owner bought?

StartLayout Enlarged Left-Brace 1st Row x + y = 4,000 2nd Row 10 x + 4 y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row 10 x + 4 y = 4,000 2nd Row x + y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row x + y = 4,000 2ndRow 0.1 x + 0.04 y = 352 EndLayout

StartLayout Enlarged Left-Brace 1st Row 0.1 x + 0.04 y = 4,000 2nd Row x + y = 352 EndLayout

Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

f(x) = x(x – a)2(x – b)4

f(x) = x(x – a)3(x – b)2

f(x) = x4(x – a)(x – b)2

f(x) = x2(x – a)5(x – b)

Which statement best describes the equation x5 + x3 – 14 = 0?

The equation is quadratic in form because it is a fifth-degree polynomial.

The equation is quadratic in form because the difference of the exponent of the lead term and the exponent of the middle term is 2.

The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.

The equation is not quadratic in form because the exponent of the lead term is not the square of the exponent of the middle term.

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Mixed Degree Systems — Unit test Answers

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