Answers Adv. Algebra II S1 OriginalFactoring Polynomials Completely

Factoring Polynomials Completely — Unit test Answers

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Which expression is equivalent to ?

StartFraction x Superscript one-half baseline Over y z squared EndFraction

StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction

StartFraction y Superscript one-half Baseline Over x z squared EndFraction

StartFraction x z squared Over y Superscript one-half EndFraction

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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.

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).

What values of c and d make the equation true? Assume and

c = 1, d = 3

c = 1, d = 9

c = 2, d = 8

c = 2, d = 9

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.

The area of a rectangle is (x3 – 5x2 + 3x – 15), and the width of the rectangle is (x2 + 3). If area = length × width, what is the length of the rectangle?

x + 5

x – 15

x + 15

x – 5

What values of c and d make the equation true? Assume and

c = 1, d = 3

c = 1, d = 9

c = 2, d = 8

c = 2, d = 9

The equation shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is k times the mean distance from the sun as planet X, by what factor is the orbital period increased?

k Superscript one-third

k Superscript one-half

k Superscript two-thirds

k Superscript three-halves

If (x – 5) is a factor of f(x), which of the following must be true?

A root of f(x) is x = –5.

A root of f(x) is x = 5.

Both x = –5 and x = 5 are roots of f(x).

Neither x = –5 nor x = 5 is a root of f(x).

Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V = P(1 – r)t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after years?

$2,500

$9,159

$22,827

$23,791

If 5 + 6i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

–5 – 6i

5 – 6i

6 – 5i

6 + 5i

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 expression is equivalent to ?

StartFraction x Superscript one-half baseline Over y z squared EndFraction

StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction

StartFraction y Superscript one-half Baseline Over x z squared EndFraction

StartFraction x z squared Over y Superscript one-half EndFraction

The price that a company charged for a computer accessory is given by the equation where x is the number of accessories that are produced, in millions. It costs the company $10 to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields the same profit?