Zeros Multiplicity of Polynomials

1.

Multiple Choice

3 mins

1 pt

Even Multiplicities have which of the following effects on the x-axis?

touches and bounces back

wiggle

crosses the x-axis

2.

Multiple Choice

1 min

1 pt

Which zero has an odd multiplicity?

-4

4

2

-2

3.

Multiple Choice

1 min

1 pt

Which root has even multiplicity?

1

-4

-1

2

4.

Multiple Choice

5 mins

1 pt

What is the equation in factored form of this graph?

f(x) = (x-4)(x-1)²(x+2)(x+4)

f(x) = (x-4)(x+1)²(x+2)(x+4)

f(x) = (x-4)(x-1)²(x-2)(x+4)

f(x) = (x+4)(x+1)²(x-2)(x-4)

5.

Multiple Choice

1 min

1 pt

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

0, 6, -5

6, -5

0, -6, 5

1, -6, 5

6.

Multiple Choice

1 min

1 pt

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

-2, 7 multiplicity 3

-2, 7, 3

2, -7 multiplicity 3

2, -7, 3

7.

Multiple Choice

2 mins

1 pt

What could be the function for this graph in factored form?

f(x) = (x-4)²(x+2)

f(x) = (x+4)²(x-2)

f(x) = (x-4)(x+2)²

f(x) = (x+4)(x-2)²

8.

Multiple Choice

3 mins

1 pt

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

Degree: 6

Degree: 5

Degree: 3

Degree: 2

9.

Multiple Choice

2 mins

1 pt

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

{0 mult. 3, 5, 2}

{−2 mult. 3, 3, 1}

{0 mult. 3, 3, 2}

{2 mult. 3, 3, 3}

10.

Multiple Choice

2 mins

1 pt

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

{0 mult. 3}

{0, 3, 1}

{0, −2, −1}

{−2, 3, 1}

11.

Multiple Choice

1 min

1 pt

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

-2, 3 (multiplicity 2), 4

-2 (multiplicity 2), 3, 4

2, -3 (multiplicity 2), -4

2 (multiplicity 2), -3, -4

12.

Multiple Choice

5 mins

1 pt

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4.

(x + 5)³(x - 9)²(x + 2)(x - 4)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

(x + 5)³(x - 9)²(x + 2)

(x + 5)(x - 9)(x + 2)(x - 4)

13.

Multiple Choice

5 mins

1 pt

f(x) = (x − 1)²(x + 2)(x + 4)³

f(x) = (x + 1)(x − 2)(x − 4)

f(x) = (x + 1)²(x − 2)(x − 4)³

f(x) = (x + 1)(x − 2)(x − 4)³

14.

Multiple Choice

2 mins

1 pt

What are the roots of the polynomial function?
y = 9(x + 2)(x - 7)³

-2, 7 multiplicity 3

-2, 7, 0

9, 2, -7 multiplicity 3

2, -7, 3

15.

Multiple Choice

2 mins

1 pt

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

x = -4, x = 3, x = -2

x = -4, x = 3, x = 2

x = -4, x = -3, x = 2

x = 4, x = 3, x = 2

16.

Multiple Choice

2 mins

1 pt

State the zeros of the polynomial (include multiplicity):
f(x) = x⁴(x+3)²(x - 2)

0, 3, 2

0(multiplicity of 4), -3 (multiplicity of 2), 2

-3 (multiplicity of 2), 2

0, 2 (multiplicity of 3)

17.

Multiple Choice

2 mins

1 pt

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

2 (Mult of 3), 7 (mult 1)

0, 2, 7

2 (mult of 2), 7 (mult of 3)

18.

Multiple Choice

3 mins

1 pt

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4.

(x + 5)³(x - 9)²(x + 2)(x - 4)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

(x + 5)³(x - 9)²(x + 2)

(x + 5)(x - 9)(x + 2)(x - 4)

19.

Multiple Choice

3 mins

1 pt

Even Multiplicities have which of the following effects on the x-axis?

Cross the x-axis

touches and bounces back

20.

Multiple Choice

3 mins

1 pt

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 Degree: 7

(x + 5)³(x - 9)²(x + 2)(x - 4)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

(x + 5)³(x - 9)²(x + 2)

(x + 5)(x - 9)(x + 2)(x - 4)

21.

Multiple Choice

3 mins

1 pt

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

Degree: 6

Degree: 5

Degree: 3

Degree: 2

22.

Multiple Choice

3 mins

1 pt

Please select the solution that describes if zeros crosses or turns at the x-axis for each x-intercept.

2 crosses, 1 crosses, -3 turns, -4 turns

1 crosses, -3 turns, - 4 crosses

1 crosses, -3 turns, -4 turns

1 turns, -3 crosses, -4 crosses

23.

Multiple Choice

1 min

1 pt

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

Even

Odd

None

24.

Multiple Choice

1 min

1 pt

If there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

Even

Odd

None

25.

Multiple Choice

1 min

1 pt

Odd Multiplicities have which of the following effects on the x-axis?

Cross the x-axis

Turn on the x-axis

26.

Multiple Choice

30 sec

1 pt

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

-2, 7 multiplicity 3

-2, 7, 3

2, -7 multiplicity 3

2, -7, 3

27.

Multiple Choice

5 mins

1 pt

The degree of a polynomial determines...

the maximum number of x-intercepts

the number of turning points

if the end behavior is up or down

the y-intercept

28.

Multiple Choice

1 min

1 pt

What are the zeros of the graph?

-4, -1, 2, 1 multiplicity 2

-4, -1, 1, 2

4, 1, -2, -1 multiplicity 2

4, 1, -1, -2

29.

Multiple Choice

1 min

1 pt

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

2 (Mult of 3), 7 (mult 1)

0, 2, 7

2 (mult of 2), 7 (mult of 3)

30.

Multiple Choice

45 sec

1 pt

What is the equation in factored form of this graph?

f(x) = (x-4)(x-1)²(x+2)(x+4)

f(x) = (x-4)(x+1)²(x+2)(x+4)

f(x) = (x-4)(x-1)²(x-2)(x+4)

f(x) = (x+4)(x+1)²(x-2)(x-4)

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