Answers DHS Algebra 2 VGeometric Series

Geometric Series — Unit test Answers

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Which of the following describes the roots of the polynomial function ?

–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3

–2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4

2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3

2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4

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According to the Rational Root Theorem, which is a factor of the polynomial f(x) = 3x3 – 5x2 – 12x + 20?

2x + 1

2x – 1

3x + 5

3x – 5

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.

4 inches

5 inches

9 inches

10 inches

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

f(x) = x2(x – a)2(x – b)4(x – c)

f(x) = x3(x – a)3(x – b)(x – c)2

f(x) = x4(x – a)(x – b)3(x – c)3

f(x) = (x – a)2(x – b)(x – c)6

What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?

(x + 1)(6x2 – 19x + 15)

(x + 1)2(2x – 3)

(x + 1)(3x – 2)(5x – 3)

(x + 1)(2x – 3)(3x – 5)

If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem.

(x + 2)(x + 60)

(x – 2)(x – 60)

(x – 10)(x + 2)(x + 6)

(x + 10)(x – 2)(x – 6)

Carlos graphed the system of equations that can be used to solve .What are the roots of the polynomial equation?

–3, –2, 3

–3, 2

18, 32

18, 32, 66

Which geometric series converges?

StartFraction 1 Over 81 EndFraction + StartFraction 1 Over 27 EndFraction + one-ninth + one-third + ellipsis

1 + one-half + one-fourth + one-eighth + ellipsis

Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 7 (negative 4) Superscript n minus 1

Sigma-Summation Underscript n = 1 Overscript infinity EndScripts one-fifth (2) Superscript n minus 1

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?

Option

Which statement describes the graph of this polynomial function?

The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.

The graph touches the x-axis at x = 0 and crosses the x-axis at x = 3.

The graph crosses the x-axis at x = 0 and touches the x-axis at x = –3.

The graph touches the x-axis at x = 0 and crosses the x-axis at x = –3.

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Geometric Series — Unit test Answers

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