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)

Free Preview

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

, , , 5

, 1, , 11

, , , , , 5, 11

0, , , , , , 5, 11

What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.

x = StartFraction negative 4 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction

x = StartFraction negative 7 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction

x = –7 and x = –2

x = –1 and x = 4

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

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

Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2?

f(x) = 2(x + 7)(x + 5)(x – 2)

f(x) = 2(x – 7)(x – 5)(x + 2)

f(x) = (x + 7)(x + 5)(x + 5)(x – 2)

f(x) = (x – 7)(x – 5)(x – 5)(x + 2)

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.

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?

mc015-1.jpg

mc015-2.jpg

mc015-3.jpg

mc015-4.jpg

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

What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i?

f(x) = x2 – 2x + 2

f(x) = x3 – x2 + 4x – 2

f(x) = x3 – 3x2 + 4x – 2

f(x) = x2 – x + 2

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.

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 sum of the first seven terms of the geometric series?3 + 12 + 48 + 192 + ...

4,372

12,288

16,383

65,535

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

Which statement best describes the equation (x + 5)2 + 4(x + 5) + 12 = 0?

The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u = (x + 5).

The equation is quadratic in form because when it is expanded, it is a fourth-degree polynomial.

The equation is not quadratic in form because it cannot be solved by using the quadratic formula.

The equation is not quadratic in form because there is no real solution.

Which expression is equivalent to ?

mc023-2.jpg

mc023-3.jpg

–18z – 5

–18z + 10

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

Which expression is equivalent to 3 + 4y – y(9 – 2y) + 5?

8 – 7y

mc008-1.jpg

mc008-2.jpg

mc008-3.jpg

The polynomial function is graphed below.Which is a potential rational root of f(x) at point P?

The root at point P may be .

A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his break, he paints half of the remaining unpainted portion and then takes another break. If he continues to paint half of the remaining unpainted portion between breaks, approximately what portion of the original wall will be painted when he takes his fifth break?

112.50 ft2

145.31 ft2

147.66 ft2

290.63 ft2

Which expression is equivalent to ?

mc025-2.jpg

mc025-3.jpg

mc025-4.jpg

mc025-5.jpg

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 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

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

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, ).

Unit Test Answers

More from this Course

TRY EDGENUITY HACKS