AnswersMathematics III ASynthetic Division and the Remainder Theorem

Graphing Polynomial Functions Answers

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At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x-axis?

A
–5
B
–2
C
2
D
5
2
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Which graph has the same end behavior as the graph of f(x) = –3x3 – x2 + 1?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

A polynomial function has a root of –5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the function has a negative leading coefficient and is of even degree, which statement about the graph is true?

A
The graph of the function is positive on (, –5).
Option A
B
The graph of the function is negative on (–5, 3).
C
The graph of the function is positive on (, 1).
Option C
D
The graph of the function is negative on (3, ).
Option D
4

Which graph shows the same end behavior as the graph of f(x) = 2x6 – 2x2 – 5?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

Which of the following graphs could be the graph of the function ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?

A
As , and as , .
Option A
B
As , and as , .
Option B
C
As , and as , .
Option C
D
As , and as , .
Option D
7

Which of the following describes the zeroes of the graph of f(x) = 3x6 + 30x5 + 75x4?

A
–5 with multiplicity 2 and with multiplicity 4
Option A
B
5 with multiplicity 2 and with multiplicity 4
Option B
C
–5 with multiplicity 2 and 0 with multiplicity 4
D
5 with multiplicity 2 and 0 with multiplicity 4
8

Which statement describes the graph of f(x) = 4x7 + 40x6 + 100x5?

A
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 5.
B
The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5.
C
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5.
D
The graph touches the x-axis at x = 0 and crosses the x-axis at x = –5.
9

Which statement describes the graph of f(x) = –4x3 – 28x2 – 32x + 64?

A
The graph crosses the x-axis at x = 4 and touches the x-axis at x = –1.
B
The graph touches the x-axis at x = 4 and crosses the x-axis at x = –1.
C
The graph crosses the x-axis at x = –4 and touches the x-axis at x = 1.
D
The graph touches the x-axis at x = –4 and crosses the x-axis at x = 1.
10

At which root does the graph of f(x) = (x + 4)6(x + 7)5 cross the x-axis?

A
–7
B
–4
C
4
D
7

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