Quiz about Rational and Complex Zeros of Polynomial Functions

Question 1

Find all zeros of the polynomial function P(x) = x³+6x²+9x+54

Accepted Answer

-6, 3i, -3i

Answer

6, 3, -3

Answer

-6, 3, -3

Answer

6, 3i, -3i

Question 2

Find all zeros for the polynomial function P(x)= x³-3x²+12x-10

Accepted Answer

1, 1-3i, 1+3i

Answer

1, 1+3i, -1-3i

Answer

-1, -1+3i, -1-3i

Answer

-1, -5, 2

Question 3

Find a polynomial function of degree 3 with zeros 3i and -2.

Accepted Answer

P(x) = x³+2x²+9x+18

Answer

P(x) = x³+2x²+9x+11

Answer

P(x) = x³-2x²+9x+18

Answer

P(x) = x²-3ix+2x-6i

Question 4

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4

Accepted Answer

7

Answer

4

Answer

2

Answer

11

Question 5

How many zeros does the polynomial function
P(x) = 3x⁴+4x-8 have?

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 6

How many real zeros does the polynomial function
P(x) = x³+2x²+9x+18 have?

Accepted Answer

1

Answer

0

Answer

2

Answer

3

Question 7

How many negative zeros does the polynomial function
P(x) = x³+3x²-5x-15 have?

Accepted Answer

2

Answer

0

Answer

1

Answer

3

Question 8

A polynomial function with rational coefficients of degree 3 MUST have at least 1 rational zero.

Accepted Answer

True

Answer

False

Question 9

A polynomial function with rational coefficients of degree 4 MUST have at least 1 rational zero.

Accepted Answer

False

Answer

True

Question 10

Is (x-7) a factor of (x²-5x+14)?

Accepted Answer

No

Answer

Yes

Question 11

If the binomial (x - 7) is a factor of the polynomial function f(x), which statement must be true?

Accepted Answer

f(7) = 0

Answer

f(7) = -7

Answer

f(-7) = 0

Answer

f(-7) = -7

Question 12

Factor:
x³-12x²+47x-60=0 when 5 is a root.

Accepted Answer

(x-3)(x-4)(x-5)=0

Answer

(x+1)(x-4)(x-5)=0

Answer

(x-3)(x-4)(2x-5)=0

Answer

(x-5)(x-4)(x-5)=0

Question 13

f(x) = 2x³ - 3x² + 4x -10

State the maximum number of turns the graph of f(x) could make.

Accepted Answer

2

Answer

3

Answer

1

Answer

0

Question 14

f(x) = -3x⁴ + x³ - 2x² + x - 1

What is the y-intercept of f(x)?

Accepted Answer

(0, -1)

Answer

(-1, 0)

Answer

(-3, 0)

Answer

(0, -3)

Question 15

Classify the function:

Accepted Answer

cubic

Answer

quadratic

Answer

quartic

Answer

linear

Question 16

What is another way to say "where a function crosses the x-axis"?

Accepted Answer

all of these.

Answer

x-intercept

Answer

zero

Answer

root

Question 17

If a zero of a polynomial function has multiplicity 4 that means:

Accepted Answer

The graph will "bounce back" at that zero

Answer

The x intercept is at (4, 0)

Answer

The graph will "pass through" at that zero

Answer

Zeros cannot have multiplicity of 4

Question 18

Is this division problem worked correctly?

Accepted Answer

This is incorrect!

Answer

This is correct!

Question 19

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

Accepted Answer

6   -4   0   3   1

Answer

3   0   -4   6   1

Answer

6   -4   3   1   0

Answer

-6   4   0   -3   -1

Question 20

What does it mean to be a factor of a number?

Accepted Answer

Divides evenly with a remainder of zero.

Answer

Divides unevenly with a remainder of 1.

Question 21

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

Accepted Answer

Yes, (x-2) is a factor. The remainder is zero.

Answer

Yes, (x-2) is a factor. There is a remainder.

Answer

No, (x-2) is  not a factor. The remainder is zero.

Answer

No, (x-2) is  not a factor. There is a remainder.

Question 22

How many roots or zeros does the equation
f(x) = 5x⁴-8x³+4x²-6x+3 have?

Accepted Answer

4

Answer

3

Answer

5

Answer

0

Question 23

f(x) = 2x³ - 3x² + 4x -10

What is the degree of f(x)?

Accepted Answer

3

Answer

2

Answer

1

Answer

0

Rational and Complex Zeros of Polynomial Functions

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