Answers DCSS Advanced Algebra CR 24-25Unit Test

Unit Test — Unit test Answers

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Use synthetic division to solve (x4 – 1) ÷ (x – 1). What is the quotient?

x cubed minus x squared + x minus 1

x cubed + x squared + x + 1

x3 – 2

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What is the completely factored form of x2 – 16xy + 64y2?

xy(x – 16 + 64y)

xy(x + 16 + 64y)

(x – 8y)(x – 8y)

(x + 8y)(x + 8y)

Which statement about –2h2 – 15h – 7 is true?

One of the factors is (h + 2).

One of the factors is (3h – 2).

One of the factors is (2h + 1).

One of the factors is (h – 7).

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot?

120 ft

205 ft

210 ft ✓ Correct

375 ft

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

–6, 6

–4, 1, 3

–3, –1, 4

1, 3

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.

Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 + i. 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 three real roots.

f(x) has five real roots.

f(x) has three real roots and two imaginary roots.

What are the solutions of the equation (x – 3)2 + 2(x – 3) – 8 = 0? Use u substitution to solve.

x = –5 and x = 1

x = –1 and x = 5

x = –1 and x = –7

x = 1 and x = 7

Which equation is quadratic in form?

3x5 + 8x3 + 6 = 0

6x4 + 7x2 – 3 = 0

5x6 + x4 + 12 = 0

x9 + x3 – 10 = 0

If (x – 2k) is a factor of f(x), which of the following must be true?

f(2k) = 0

f(–2k) = 0

A root of f(x) is x = –2k.

A y intercept of f(x) is x = 2k.

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

A company plans to sell pens for $2 each. The company’s financial planner estimates that the cost, y, of manufacturing the pens is a quadratic function with a y-intercept of 120 and a vertex of (250, 370). What is the minimum number of pens the company must sell to make a profit?

173

174 ✓ Correct

442

443

Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

mc012-1.jpg

mc012-2.jpg

mc012-3.jpg

mc012-4.jpg

A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?

The graph of the function is positive on (–6, –2).

The graph of the function is negative on (, 0).

The graph of the function is positive on (–2, 4).

The graph of the function is negative on (4, ).

The price that a company charged for a basketball hoop is given by the equation where x is the number of hoops that are produced, in millions. It costs the company $30 to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

1.3 million hoops

1.4 million hoops

15 million hoops

30 million hoops

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

She is incorrect because systems may have only complex solutions which are not visible on a graph.

She is incorrect because the solutions may have multiplicity greater than 1.

She is correct because all solutions are intersection points of the graphs.

She is correct because the solutions are irrational.

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

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

–3 + 2i, –3 – 2i

–2, –4

–2, –4, –3 + 2i, –3 – 2i

–2, –4, –3 + 2i, 3 + 2i

A student factors 10x2 + 3x – 27 to the following. (2x – 3)(5x + 9) Which statement about (2x – 3)(5x + 9) is true?

The expression is equivalent, and it is completely factored.

The expression is equivalent, but it is not completely factored.

The expression is not equivalent, but it is completely factored.

The expression is not equivalent, and it is not completely factored.

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

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