Polynomials: Master the Basics and Beyond

Question 1

Which of the following is NOT a characteristic of polynomials?

Accepted Answer

Fractional coefficients

Answer

Whole number exponents

Answer

Constant coefficients

Answer

Variable terms

Question 2

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

Accepted Answer

2x^2 - 7x - 15

Answer

2x^2 + 7x - 15

Answer

2x^2 - 15

Answer

2x^2 + 15

Question 3

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 4

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

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 5

Simplify the expression: (3x^2y)^-2

Accepted Answer

1/9x^4y^2

Answer

9x^4y^2

Answer

9x^2y^-4

Answer

1/9x^2y^-4

Question 6

Which of the following expressions is a polynomial?

Accepted Answer

x² + 3x - 5

Answer

(x + 2)/(x - 3)

Answer

sin(x)

Answer

1/x

Question 7

Factor the polynomial expression: x² - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x + 3)(x + 3)

Answer

The expression cannot be factored.

Question 8

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

Accepted Answer

5

Answer

2

Answer

3

Answer

4

Question 9

Which of the following is a zero of the polynomial x² - 4?

Accepted Answer

Both 2 and -2

Answer

0

Answer

2

Answer

-2

Question 10

Simplify the expression: (2x + 3)(x - 2)

Accepted Answer

2x² - x - 6

Answer

2x² + x - 6

Answer

2x² - 7x - 6

Answer

2x² + 7x - 6

Question 11

Which of the following represents the graph of a quadratic polynomial?

Accepted Answer

A parabola

Answer

A straight line

Answer

A circle

Answer

A hyperbola

Question 12

Which of the following expressions is a polynomial?

Accepted Answer

2x^3 + 5x - 7

Answer

x^2 - 2/x + 1

Answer

sin(x) + cos(x)

Answer

e^x + ln(x)

Question 13

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

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 14

Which of the following is the graph of the polynomial function f(x) = x^3 - 2x^2 + 1?

Accepted Answer

A cubic function with a local minimum and maximum

Answer

A parabola opening up

Answer

A parabola opening down

Answer

A linear function with a positive slope

Question 15

What is the leading coefficient of the polynomial 4x^5 - 3x^3 + 2x - 1?

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 16

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

Accepted Answer

1

Answer

-1

Answer

2

Answer

3

Question 17

Factor the polynomial completely: **x^2 - 9**

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x - 3)^2

Answer

(x + 3)^2

Question 18

Which of the following polynomials is monic?

Accepted Answer

x^2 + 2x + 1

Answer

2x^2 + 3x - 4

Answer

x^3 - 2x^2 + 5x - 10

Answer

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

Question 19

Which of the following is a theorem that relates the roots of a polynomial to its coefficients?

Accepted Answer

Vieta's Formulas

Answer

Descartes' Rule of Signs

Answer

The Remainder Theorem

Answer

The Factor Theorem

Question 20

Which of the following expressions represents a polynomial?

Accepted Answer

x^2 - 2y + 5

Answer

sqrt(x) + y^2

Answer

e^(x^2) - 1

Answer

sin(2x) + cos(3y)

Question 21

Identify the polynomial function whose graph has 2 x-intercepts and 1 y-intercept

Accepted Answer

y = x^2 - 4x + 3

Answer

y = x^3 - 2x^2 + x

Answer

y = x^4 - 3x^2 + 2x

Answer

y = x^5 - 4x^3 + 3x

Question 22

Identify the polynomial expression:

Accepted Answer

x^2 + 2x - 3

Answer

cos(x)

Answer

e^x

Answer

√(x+2)

Question 23

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

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 24

Match the polynomial function to its equation:

Accepted Answer

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

Answer

f(x) = x^2 - 4x + 3: y = (x + 2)^2 - 1

Answer

f(x) = x^2 - 4x + 3: y = (x - 1)^2 + 6

Answer

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

Question 25

Identify the polynomial that is a trinomial.

Accepted Answer

x^2 + 2x + 1

Answer

x^3 + 2x^2 + x

Answer

x + 2

Answer

2x^2 + x

Question 26

Factor the following quadratic polynomial: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 1)

Answer

Prime

Answer

(x - 3)^2

Question 27

Determine the remainder when x^3 - 2x^2 + x - 2 is divided by x - 1.

Accepted Answer

-1

Answer

1

Answer

2

Answer

0

Question 28

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

Accepted Answer

4

Answer

1

Answer

3

Answer

2

Question 29

Identify the leading coefficient of the polynomial: -2x^3 + 5x^2 - 7x + 1

Accepted Answer

-2

Answer

5

Answer

-7

Answer

1

Question 30

Which of the following is NOT a characteristic of polynomials?

Accepted Answer

They can have fractional exponents.

Answer

They can be multiplied by monomials according to the distributive property.

Answer

They can be added and subtracted like monomials.

Answer

They can be divided by monomials without remainder.

Question 31

What is the highest exponent of the variable in the polynomial 3x^3 - 2x^2 + 5x + 1?

Accepted Answer

3

Answer

4

Answer

2

Answer

5

Question 32

Identify the leading coefficient of the polynomial expression 2x^3 - 5x^2 + 3x - 1.

Accepted Answer

2

Answer

3

Answer

-5

Answer

1

Question 33

When the polynomial x^3 - 2x^2 + 3x - 4 is divided by (x - 1), what is the remainder?

Accepted Answer

-1

Answer

0

Answer

1

Answer

2

Question 34

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

Accepted Answer

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

Answer

f(x) = sin(x)

Answer

f(x) = |x|

Answer

f(x) = e^x

Question 35

What is the degree of the polynomial 3x^4 - 2x^2 + 5x - 1?

Accepted Answer

4

Answer

3

Answer

2

Answer

1

Question 36

Which of the following is a monomial?

Accepted Answer

7x^3

Answer

4x^2 - 9

Answer

x^4 - 3x + 1

Answer

2x^2 + 5x

Question 37

Factor the expression x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 9)(x - 1)

Answer

(x + 3)(x + 3)

Answer

(x + 9)(x - 1)

Question 38

What are the roots of the quadratic equation x^2 - 4x + 3 = 0?

Accepted Answer

x = 1, x = 3

Answer

x = 2, x = 6

Answer

x = -1, x = -3

Question 39

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

Accepted Answer

x - 2

Answer

x - 4

Answer

x + 2

Answer

x + 4

Question 40

The graph of a polynomial function always passes through the origin.

Accepted Answer

False

Answer

N/A

Answer

True

Answer

N/A

Question 41

A polynomial function with a leading coefficient of 1 and a degree of 3 has at most how many real roots?

Accepted Answer

3

Answer

4

Answer

2

Question 42

Which of the following is NOT a polynomial?

Accepted Answer

2x^2 + 1/x - 3

Answer

7x^5 - 3x^2 + 9

Answer

x^3 - 5x + 2

Answer

4x^4 - 2x^2 + 1

Question 43

What is the degree of the polynomial 5x^3 - 2x^2 + 7x - 1?

Accepted Answer

3

Answer

1

Answer

4

Answer

2

Question 44

Which of the following is a quadratic polynomial?

Accepted Answer

3x^2 + 2x - 1

Answer

x^3 - 5x + 2

Answer

4x^4 + 3x^2

Question 45

Simplify the expression (2x + 3)(x - 5)

Accepted Answer

2x^2 - 7x - 15

Answer

2x^2 + 7x - 15

Answer

2x^2 + 13x - 15

Answer

2x^2 - 13x - 15

Question 46

Factor the expression x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x + 3)^2

Answer

(x + 9)(x - 9)

Question 47

What are the roots of the quadratic equation x^2 - 4x + 3 = 0?

Accepted Answer

x = 1, x = 3

Answer

x = -2, x = -1

Answer

x = -1, x = -3

Answer

x = 2, x = 1

Question 48

What is the value of the polynomial 2x^3 + 5x - 1 when x = 2?

Accepted Answer

23

Answer

21

Answer

19

Answer

15

Question 49

Which of the following is the standard form of the polynomial (x + 2)^3?

Accepted Answer

x^3 + 6x^2 + 12x + 8

Answer

x^3 + 8

Answer

x^3 + 6x^2 + 6x + 8

Answer

x^3 + 3x^2 + 6x + 8

Question 50

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

Accepted Answer

5x^2 + 2x + 4

Answer

5x^2 - 6x + 6

Answer

x^2 + 2x + 4

Answer

5x^2 - 2x + 4

Question 51

Which of the following expressions represents the difference of the polynomials 4x^3 - 2x^2 + 5 and x^3 + 3x^2 - 1?

Accepted Answer

3x^3 - 5x^2 + 6

Answer

3x^3 - x^2 + 6

Answer

3x^3 + 5x^2 + 6

Answer

3x^3 + x^2 + 4

Question 52

The graph of the polynomial function y = x^2 - 4x + 3 intersects the x-axis at which points?

Accepted Answer

x = 1 and x = 3

Answer

x = 2 and x = 1

Answer

x = -2 and x = -1

Answer

x = -1 and x = -3