Question 1

How should the polynomial function f(x) = 2x + x³ + 3x⁵ + 4 be written in standard form?

Accepted Answer

f(x) = 3x⁵+ x³ + 2x + 4

Answer

f(x) = 4 + 2x + 3x⁵ + x³

Answer

f(x) = 4 + 3x⁵ + 2x + x³

Answer

f(x) = x³ + 2x + 3x⁵ + 4

Question 2

Which of the following is the factored form of the polynomial f(x) = x⁵ + 6x⁴+ 11x³ + 2x² − 12x – 8?

Accepted Answer

y = (x - 1)(x + 1)(x + 2)³

Answer

y = (x + 1)(x + 1)(x + 2)

Answer

y = (x + 1)(x + 1)(x + 2)³

Answer

y = (x - 1)(x + 1)(x + 2)

Question 3

What are the x-intercepts of the polynomial function f(x) = (x-1)(x-2)(x+3)?

Accepted Answer

(1,0), (2,0), (-3,0)

Answer

(-1,0), (-2,0) (-3,0)

Answer

(1,0), (2,0), (3,0)

Answer

(-1,0), (-2,0), (3,0)

Question 4

What is the y-intercept of the function f(x) = (x-1)³(x-2)²(x+3)?

Accepted Answer

(0&#44;-12)

Answer

(0&#44;-6)

Answer

(0&#44;12)

Answer

(0&#44;6)

Question 5

What is the behavior of the graph with a polynomial function f(x) = 2x³ + 10x² + 6x + 25?

Accepted Answer

The graph falls on the left and rises on the right.

Answer

The graph rises on the left and rises on the right.

Answer

The graph falls on the left and falls on the right.

Answer

The graph rises on the left and falls on the right.

Question 6

What is the behavior of the graph with a polynomial function f(x) = -3x⁴ + 8x² + 12x + 5?

Accepted Answer

The graph falls on the left and falls on the right.

Answer

The graph rises on the left and rises on the right

Answer

The graph rises on the left and falls on the right

Answer

The graph falls on the left and rises on the right

Question 7

What is the behavior of the graph with a polynomial function f(x) = (-x-1)³(x-2)²(-x+3)?

Accepted Answer

The graph rises on the left and rises on the right

Answer

The graph falls on the left and rises on the right

Answer

The graph falls on the left and falls on the right

Answer

The graph rises on the left and falls on the right

Question 8

What is the multiplicity of the root 1 in this polynomial function f(x) = (x-1)³ (x-2)²?

Accepted Answer

3; odd

Answer

3; even

Answer

2; even

Answer

2; odd

Question 9

If you will draw the graph of f(x) = (x-1)³ (x-2)², how will you sketch it with respect to x-axis?

Accepted Answer

Sketch it crossing (1,0) and tangent at (2,0)

Answer

Sketch it tangent at (1,0) and crossing (2,0)

Answer

Sketch it crossing both (1,0) and (2,0)

Answer

Sketch it tangent at both (1,0) and (2,0)

Question 10

What are the intervals if for the polynomial function f(x) = (x-1)(x-2)(x+3)?

Accepted Answer

x < -3, -3 < x < 1, 1 < x < 2, and x > 2

Answer

x < 3, 3 < x < -1, -1 < x < -2, and x > -2

Answer

x < 1, 1 < x < 2, 2 < x < 3, and x > 3

Answer

x < -1, -1 < x < -2, -2 < x < 3, and x > 3

Question 11

If the interval is -8 < x < 0, which of the following test values does not satisfy the condition?

Accepted Answer

1

Answer

-4

Answer

-2

Answer

-3

Question 12

If the interval is x > 3, which of the following test values does not satisfy the condition?

Accepted Answer

3

Answer

4

Answer

5

Answer

6

Question 13

Your friend Manuel encounters difficulties in showing a sketch of the graph of y = 2x³ + 3x² – 4x – 6. You know that the quickest technique is the Leading Coefficient Test. You want to help him in his problem. What hint/clue should you give?

Accepted Answer

The graph falls to the left and rises to the right

Answer

The graph falls to both left and right

Answer

The graph rises to both left and right

Answer

The graph rises to the left and falls to the right

Question 14

Emma was asked to rewrite the given polynomial function f(x) = 2x + 3x³ + 3x⁵ – 4x² – 22 in standard form. Her answer is shown below.

f(x) = 2x + 3x³+ 3x⁵ – 4x² – 22 -> f(x) = 3x⁵ + 3x³ – 4x² + 2x – 22.

Did Emma write the polynomial function in standard form correctly?

Accepted Answer

Yes, the terms are complete, signs are correct, and the degree of x is in descending order.

Answer

Yes, the terms are complete, signs are correct, and the degree of x is in ascending order.

Answer

No, some part of her solution is incorrect.

Answer

Yes, but it is not written in an order.

Question 15

Which of the following could be the graph of the polynomial function y = x³ – 4x²+ 3x – 12?

Accepted Answer

https://uploads.quizalize.com/0de080e7-7598-4836-b1b4-90879c48fa6e/question/b53a8a2799031c91c1501dd6928e55031f3b149d.png

Answer

https://uploads.quizalize.com/0de080e7-7598-4836-b1b4-90879c48fa6e/question/934b41573f7cb2da8ec704a541f66ba962a3ed81.png

Answer

https://uploads.quizalize.com/0de080e7-7598-4836-b1b4-90879c48fa6e/question/76d8f0acbd8e7cca6536c796703e2189a6e6239b.png

Answer

https://uploads.quizalize.com/0de080e7-7598-4836-b1b4-90879c48fa6e/question/dd902814cace3fabd78384dd7b2a8624fb122f3b.png

Question 16

If you will draw the graph of the polynomial function f(x) = x(x-2)², how will you sketch it with respect to x-axis?

Accepted Answer

Sketch it crossing (0,0) and tangent at (2,0)

Answer

Sketch it crossing both (0,0) and (2,0)

Answer

Sketch it tangent at both (0,0) and (2,0)

Answer

Sketch it tangent at (0,0) and crossing (2,0)

Question 17

What is the behavior of the graph relative to x-axis if the interval’s sign is negative?

Accepted Answer

The curve is below the x-axis

Answer

The right hand is falling

Answer

The curve is above the x-axis

Answer

The right hand is rising

Question 18

Given the graph on the right&#44; what can you say about the leading coefficient
and the degree of this polynomial function?

Accepted Answer

Positive and even

Answer

Negative and odd

Answer

Negative and even

Answer

Positive and odd

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