Polynomials: Operations, Factoring, and Graphing

Question 1

Which expression is a polynomial?

Accepted Answer

x^2 + 2x - 3

Answer

1/x + 2

Answer

sin(x)

Answer

e^x

Question 2

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

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 3

If f(x) = x^3 - 2x^2 + 5 and g(x) = x - 1, what is (fg)(x)?

Accepted Answer

x^4 - 3x^3 + 7x - 5

Answer

x^4 - 2x^3 + 5x

Answer

x^3 - 3x^2 + 7x - 5

Answer

x^3 - 2x^2 + 6x - 5

Question 4

What is the graph of the polynomial y = x^2 - 2x + 1 called?

Accepted Answer

Parabola

Answer

Linear equation

Answer

Hyperbola

Answer

Exponential function

Question 5

What is the leading coefficient of the polynomial 3x^3 - 2x^2 + 5?

Accepted Answer

3

Answer

2

Answer

5

Answer

-5

Question 6

Which of the following expressions represents a polynomial?

Accepted Answer

x^2 + 2x - 1

Answer

2x + 3y - 5

Answer

√x + 5

Answer

sin(x) + cos(x)

Question 7

Factor the polynomial x^2 - 4.

Accepted Answer

(x - 2)(x + 2)

Answer

(x + 2)^2

Answer

(x - 2)^2

Answer

Cannot be factored

Question 8

Which expression is equivalent to (x^2 - 4)^3?

Accepted Answer

x^6 - 12x^4 + 48x^2 - 64

Answer

x^6 + 12x^4 + 48x^2 + 64

Answer

(x - 2)^3(x + 2)^3

Answer

(x - 2)^9(x + 2)^9

Question 9

Which of the following functions is a rational function?

Accepted Answer

x/(x - 1)

Answer

x^2 + 1

Answer

e^x

Answer

sin(x)

Question 10

Determine the degree of the polynomial: 3x⁵ - 2x³ + x

Accepted Answer

5

Answer

1

Answer

3

Answer

7

Question 11

Factor the polynomial: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)^2

Answer

(x - 8)(x + 8)

Answer

x(x - 4)

Question 12

Which statement is true about the end behavior of the polynomial f(x) = -x^4 + 2x^3 - x + 1?

Accepted Answer

As x approaches infinity, f(x) approaches negative infinity.

Answer

As x approaches infinity, f(x) approaches positive infinity.

Answer

As x approaches negative infinity, f(x) approaches negative infinity.

Answer

As x approaches negative infinity, f(x) approaches positive infinity.

Question 13

Identify the polynomial:

Accepted Answer

x^2 + 3x - 5

Answer

(x + 2)/(x - 1)

Answer

sin(x)

Answer

e^x

Question 14

When a polynomial with real coefficients has complex roots, which of the following must be true about its coefficients?

Accepted Answer

At least one coefficient is not real.

Answer

The leading coefficient is negative.

Answer

All coefficients are rational.

Question 15

Which of the following is NOT a term in the polynomial 3x^2 - 5xy + 2y^3?

Accepted Answer

4xy

Answer

3x^2

Answer

5xy

Answer

2y^3

Question 16

Which of the following is a factor of the polynomial x^3 - 8?

Accepted Answer

x - 2

Answer

x + 2

Answer

x^2 - 4

Answer

x^2 + 4

Question 17

Which of the following is the degree of the polynomial x^4 - 2x^2 + 5?

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 18

Which of the following is a factor of the polynomial x^3 - 2x^2 + x - 2?

Accepted Answer

x - 2

Answer

x + 2

Answer

x + 1

Answer

x - 1

Question 19

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

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 20

Factor the following polynomial: x² - 9.

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)

Answer

(x + 3)²

Answer

(x - 3)²

Question 21

Which of the following is a factor of the polynomial x^2 - 9?

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x + 3)^2

Answer

(x + 2)(x - 2)

Question 22

Which polynomial has a degree of 4?

Accepted Answer

5x^4 - 2x^2 + 7x - 3

Answer

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

Answer

2x + 5

Answer

x^2 - 3x + 2

Question 23

Which of the following terms are NOT a term of the polynomial 3x^2 + 5x - 2?

Accepted Answer

x

Answer

5x

Answer

3x^2

Question 24

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

Accepted Answer

4

Answer

5

Answer

2

Answer

3

Question 25

Which of the following is the leading coefficient of the polynomial: -2x^3 + 4x^2 - 3x + 1?

Accepted Answer

-2

Answer

4

Answer

-3

Answer

1

Question 26

Which of the following expressions is a polynomial?

Accepted Answer

x^3 - 2x + 5

Answer

x^(1/2) - 2

Answer

sin(x) + cos(x)

Answer

e^x + 1

Question 27

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

Accepted Answer

3x^2 - 5x + 6

Answer

x^3 - 2x^2 - 4x + 6

Answer

2x^3 - x^2 - x + 6

Answer

x^2 - x + 6

Question 28

Factor the following polynomial: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x + 2)^2

Answer

(x - 4)(x + 1)

Answer

Not factorable

Question 29

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

Accepted Answer

4

Answer

3

Answer

1

Answer

2

Question 30

Determine whether the polynomial x^3 - 2x^2 + 1 is monic:

Accepted Answer

True

Answer

False

Answer

Cannot be determined

Question 31

Which of the following expressions is a polynomial in terms of x?

Accepted Answer

x^3 - 2x^2 + x - 5

Answer

e^x

Answer

sin(x)

Question 32

Factor the polynomial completely: x^2 - 16

Accepted Answer

(x + 4) (x - 4)

Answer

Cannot be factored

Answer

(x - 8) (x + 2)

Answer

(x - 4)^2

Question 33

Which of the following is the graph of the polynomial y = x^2 + 2x - 3?

Accepted Answer

A parabola opening upwards with vertex at (-1, -4)

Answer

A parabola opening downwards with vertex at (1, 4)

Answer

A straight line with slope 1

Answer

A circle centered at the origin

Question 34

Which of the following polynomial functions has a degree of 3?

Accepted Answer

f(x) = 2x^3 - x^2 + 4x - 3

Answer

f(x) = 1 / x

Answer

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

Answer

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

Question 35

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

Accepted Answer

4

Answer

3

Answer

2

Answer

1

Question 36

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

Accepted Answer

4x² + 2x + 2

Answer

4x⁴ + 2x² + 2

Answer

4x² - 2x + 8

Answer

x² + 2x + 2

Question 37

What is the product of (x - 5) and (x + 3)?

Accepted Answer

x² - 2x - 15

Answer

x² - 8x - 15

Answer

x² + 2x - 15

Answer

x² + 8x - 15

Question 38

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

Accepted Answer

6

Answer

-1

Answer

2

Answer

1

Question 39

What is the y-intercept of the graph of the polynomial y = 2x² - 5x + 3?

Accepted Answer

3

Answer

2

Answer

-3

Answer

-2

Question 40

Which of the following polynomials has a zero at x = 3?

Accepted Answer

x² - 6x + 9

Answer

x² - 3x + 9

Answer

x² - 9x + 3

Answer

x² + 3x + 9

Question 41

What is the leading coefficient of the polynomial -5x³ + 2x² + 7x - 1?

Accepted Answer

-5

Answer

2

Answer

3

Question 42

A rectangle has a length of (x + 5) and a width of (x - 2). What is the area of the rectangle?

Accepted Answer

x² + 3x - 10

Answer

x² - 3x - 10

Answer

x² + 7x - 10

Question 43

The graph of a polynomial function has a local minimum at the point (2, -3). What can you conclude about the polynomial?

Accepted Answer

The polynomial has an even degree and a positive leading coefficient.

Answer

The polynomial has an even degree and a negative leading coefficient.

Answer

The polynomial has an odd degree and a positive leading coefficient.

Question 44

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

Accepted Answer

3

Answer

5

Answer

1

Answer

2

Question 45

Which of the following is a polynomial?

Accepted Answer

3x^2 - 5x + 2

Answer

√x + 1

Answer

x^-2 + 3x

Answer

1/x - 4

Question 46

Simplify the expression (2x + 3)(x - 1).

Accepted Answer

2x^2 + x - 3

Answer

2x^2 + 5x - 3

Answer

2x^2 - 3

Answer

2x^2 - x - 3

Question 47

What is the result of dividing (x^3 + 2x^2 - 5x - 6) by (x + 2)?

Accepted Answer

x^2 - 5

Answer

x^2 + 2x - 5

Answer

x^2 + 4x - 5

Answer

x^2 - 5x + 6

Question 48

Factor the polynomial x^2 - 9.

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x - 9)(x + 1)

Answer

(x + 3)^2

Question 49

Which of the following is the factored form of 2x^2 + 5x - 3?

Accepted Answer

(2x - 1)(x + 3)

Answer

(2x + 1)(x - 3)

Answer

(x - 1)(2x + 3)

Answer

(x + 1)(2x - 3)

Question 50

What is the sum of the polynomials 3x^2 - 2x + 1 and 2x^2 + 5x - 4?

Accepted Answer

5x^2 + 3x - 3

Answer

5x^2 + 7x - 3

Answer

x^2 + 7x + 5

Answer

x^2 + 3x - 3

Question 51

What is the difference between the polynomials 4x^3 - 2x^2 + 5 and 2x^3 + x^2 - 3?

Accepted Answer

2x^3 - 3x^2 + 8

Answer

2x^3 - 3x^2 + 2

Answer

6x^3 - x^2 + 2

Answer

2x^3 + 3x^2 + 8

Question 52

What is the value of the polynomial 2x^2 - 3x + 1 when x = 2?

Accepted Answer

3

Answer

9

Answer

1

Answer

5

Question 53

Which of the following graphs represents the polynomial y = x^2 - 4?

Accepted Answer

A graph that is a parabola opening upwards, intersecting the x-axis at -2 and 2.

Answer

A graph that is a parabola opening downwards, intersecting the x-axis at -2 and 2.

Answer

A graph that is a straight line.