Master Polynomials: Operations, Factoring, and Remainder Theorem

Question 1

Which of these is NOT a type of polynomial?

Accepted Answer

Rational function

Answer

Monomial

Answer

Binomial

Answer

Trinomial

Question 2

Which of the following expressions is a polynomial?

Accepted Answer

3x^2 - 2x + 1

Answer

2x / (x - 1)

Answer

sqrt(x) + 3

Answer

sin(x) + x

Question 3

What is the degree of the polynomial 2x^4 + 4x^2 - 6?

Accepted Answer

4

Answer

3

Answer

1

Answer

2

Question 4

Which of the following is equivalent to (x + 2)(x - 3)?

Accepted Answer

x^2 - x - 6

Answer

x^2 + x - 6

Answer

x^2 - 7x - 6

Answer

x^2 + 5x - 6

Question 5

Which of the following is an example of a polynomial function?

Accepted Answer

f(x) = 2x^3 - 5x^2 + 3x + 1

Answer

f(x) = sqrt(x) + 3

Answer

f(x) = sin(x)

Answer

f(x) = 2x / (x - 1)

Question 6

What is the vertical asymptote of the rational function f(x) = (x^2 - 4) / (x - 2)?

Accepted Answer

x = 2

Answer

x = -4

Answer

x = 4

Answer

x = -2

Question 7

Which of the following expressions is NOT a polynomial?

Accepted Answer

(x+1)/(x-2)

Answer

2x^3 - x^2 + 5

Answer

3x^4 - 2x^3 + 5x^2 - x + 1

Answer

x^2 - 4x + 3

Question 8

Simplify the following polynomial: (2x^2 - 3x + 1) + (x^2 + 2x - 4)

Accepted Answer

3x^2 - x - 3

Answer

x^2 - x - 3

Answer

3x^2 + x - 3

Question 9

Factor the following polynomial completely: x^3 - 8

Accepted Answer

(x - 2)(x^2 + 2x + 4)

Answer

Cannot be factored

Answer

(x - 2)^3

Answer

(x + 2)(x^2 - 2x + 4)

Question 10

Find the remainder when the polynomial x^3 - 5x^2 + 7x - 3 is divided by (x - 3) using synthetic division.

Accepted Answer

3

Answer

-3

Answer

1

Question 11

What is the degree of the polynomial 4x^5 - 3x^3 + 2x^2 - 7?

Accepted Answer

5

Answer

2

Answer

7

Answer

3

Question 12

Multiply the following polynomials: (x - 1)(x^2 + x - 2)

Accepted Answer

x^3 - 2x^2 + x + 2

Answer

x^3 - x^2 + x + 2

Answer

x^3 + x^2 - x + 2

Answer

x^3 + 2x^2 + x - 2

Question 13

Which of the following is a polynomial function?

Accepted Answer

f(x) = 5x^4 - 2x^3 + 7x - 1

Answer

f(x) = e^x

Answer

f(x) = |x|

Answer

f(x) = sin(x) + cos(x)

Question 14

Find the end behavior of the polynomial f(x) = 3x^4 - 2x^2 + 5 as x approaches infinity and negative infinity.

Accepted Answer

Up and to the right, down and to the left

Answer

Up and to the left, down and to the right

Answer

Down and to the right, up and to the left

Answer

Down and to the left, up and to the right

Question 15

Find the degree of the polynomial 2x^5 - 3x^3 + 5x - 1. The degree of a polynomial is the highest exponent of the variable in the polynomial.

Accepted Answer

5

Answer

3

Answer

4

Answer

6

Question 16

Which of the following is a trinomial? A trinomial is a polynomial with three terms.

Accepted Answer

x^2 + 2x + 1

Answer

x^2y

Answer

x^2

Answer

2x + 3y

Question 17

Factor the polynomial x^2 - 9.

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x - 3)

Answer

(x + 3)(x + 3)

Question 18

Find the remainder when x^3 - 2x^2 + 5x - 8 is divided by (x - 1) using synthetic division or the Remainder Theorem.

Accepted Answer

-5

Answer

8

Answer

0

Question 19

Classify the polynomial h(x) = 5x^4 - 3x^2 + 2 as even, odd, or neither.

Accepted Answer

Even

Answer

Neither

Answer

Odd

Answer

Not enough information

Question 20

Factor the polynomial: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 3)(x - 3)

Answer

Cannot be factored

Answer

(x - 9)(x + 1)

Question 21

Simplify the polynomial: (2x^2 - 3x + 1) + (x^2 - 2x + 5)

Accepted Answer

3x^2 - 5x + 6

Answer

x^3 - 5x^2 + 6

Answer

2x^2 - x + 6

Answer

3x^2 - 7x + 4

Question 22

Divide the polynomial: (x^3 - 2x^2 + x - 2) by the binomial (x - 1) using long division.

Accepted Answer

x^2 - x + 2

Answer

x^2 + x + 2

Answer

x^2 + 2x + 2

Answer

x^2 - 2x + 2

Question 23

Which of the following is the graph of the polynomial **y = x^2 - 4**?

Accepted Answer

A parabola opening upwards

Answer

A parabola opening downwards

Answer

A line with a negative slope

Answer

A line with a positive slope

Question 24

Factor the polynomial **x^2 - 5x + 6**.

Accepted Answer

(x - 2)(x - 3)

Answer

(x - 2)(x + 3)

Answer

(x + 2)(x + 3)

Answer

(x + 2)(x - 3)

Question 25

Simplify the following expression: (x² - 2x + 3) + (2x² + 5x - 1)

Accepted Answer

3x² + 3x + 2

Answer

x² + 3x - 2

Answer

3x² - 3x + 2

Answer

3x² - 3x - 2

Question 26

Factor the following polynomial: x² - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x + 4)(x - 4)

Answer

(x - 2)²

Answer

Cannot be factored

Question 27

Factor the following polynomial: x³ - 8

Accepted Answer

(x - 2)(x² + 2x + 4)

Answer

(x - 2)³

Answer

(x + 2)(x² - 2x + 4)

Answer

Cannot be factored

Question 28

What is the degree of the polynomial: 5x⁴ - 2x³ + 7x² - 3x + 1?

Accepted Answer

4

Answer

3

Answer

5

Question 29

Find the leading coefficient of the polynomial: -3x⁵ + 2x³ - 5x + 7?

Accepted Answer

-3

Answer

5

Answer

7

Answer

2

Question 30

Which of the following expressions represents a polynomial function?

Accepted Answer

f(x) = 2x^3 - 5x^2 + 7x - 1

Answer

f(x) = e^x

Answer

f(x) = sin(x)

Question 31

Find the degree of the polynomial f(x) = 3x^4 - 2x^3 + 5x^2 - 7x + 1.

Accepted Answer

4

Answer

3

Answer

5

Answer

7

Question 32

Factor the polynomial f(x) = x^2 - 9.

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x + 9)(x - 9)

Answer

Cannot be factored further (prime)

Question 33

For a polynomial to be divisible by (x - 2), what is a necessary condition?

Accepted Answer

f(2) = 0

Answer

The constant term is 0.

Answer

The coefficient of x^2 is 2.

Question 34

Determine the end behavior of the polynomial f(x) = -x^5 + 2x^3 - x + 4.

Accepted Answer

As x → ∞, f(x) → -∞; as x → -∞, f(x) → ∞

Answer

As x → ∞, f(x) → -∞; as x → -∞, f(x) → -∞

Answer

As x → ∞, f(x) → 4; as x → -∞, f(x) → 4

Answer

As x → ∞, f(x) → ∞; as x → -∞, f(x) → ∞

Question 35

Find the degree of the polynomial 3x^4 - 2x^3 + 5x - 1:

Accepted Answer

4

Answer

5

Answer

2

Answer

3

Question 36

Find the zeros of the polynomial f(x) = x^2 - 5x + 6:

Accepted Answer

2, 3

Answer

-2, -3

Answer

2, -3

Answer

-2, 3

Question 37

Determine if the polynomial x^4 - 1 is an odd or even function.

Accepted Answer

Even

Answer

Odd

Answer

Cannot be determined

Answer

Neither even nor odd

Question 38

Solve the polynomial inequality x^2 - 5x + 6 < 0:

Accepted Answer

2 < x < 3

Answer

x > 3 or x < 2

Answer

x < 2 or x > 3

Answer

x > 2 or x < 3

Question 39

What is the degree of the polynomial:  7x⁴ - 3x² + 2x - 5?

Accepted Answer

4

Answer

7

Answer

3

Question 40

Simplify the following polynomial expression: (3x² - 5x + 2) + (x² + 2x - 4)

Accepted Answer

4x² - 3x - 2

Answer

4x² - 7x + 6

Answer

3x² - 3x - 2

Question 41

Multiply the following polynomials: (x - 3)(x + 2)

Accepted Answer

x² - x - 6

Answer

x² - 6

Answer

x² + x - 6

Answer

x² - x + 6

Question 42

Factor the following polynomial completely: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x - 3)

Answer

(x + 9)(x - 1)

Question 43

What is the remainder when the polynomial  x³ + 2x² - 5x + 3 is divided by (x - 2)?

Accepted Answer

9

Answer

-9

Answer

-5

Answer

5

Question 44

Which of the following is NOT a factor of the polynomial x³ - 8?

Accepted Answer

(x + 2)

Answer

(x³ - 2x² + 4x - 8)

Answer

(x - 2)

Answer

(x² + 2x + 4)

Question 45

If (x - 3) is a factor of the polynomial x² - kx + 6, what is the value of k?

Accepted Answer

5

Answer

2

Answer

-5

Question 46

What is the leading coefficient of the polynomial: -2x⁵ + 7x³ - 4x + 9?

Accepted Answer

-2

Answer

7

Answer

5

Answer

9

Question 47

A rectangular garden has a length of (x + 5) meters and a width of (x - 2) meters. What is the area of the garden in square meters?

Accepted Answer

x² + 3x - 10

Answer

2x + 10

Answer

x² + 7x - 10

Answer

2x + 3

Question 48

Which of the following is a polynomial function?

Accepted Answer

f(x) = 3x² - 2x + 1

Answer

f(x) = √x - 3

Answer

f(x) = 4^x + 2

Answer

f(x) = 2/x + 1