Polynomials: Operations, Factoring, and Applications

Question 1

Which of the following expressions is NOT a polynomial?

Accepted Answer

2 / (x - 1)

Answer

x^2 + 3x + 2

Answer

x^3 - 2x^2 + 4

Answer

(x + 1)^2

Question 2

The leading coefficient of the polynomial -2x^4 + 5x^3 - 3x^2 + 1 is:

Accepted Answer

-2

Answer

5

Answer

-3

Answer

1

Question 3

Add the polynomials: (x^2 - 2x + 3) + (x^2 + 3x - 5)

Accepted Answer

2x^2 + x + 2

Answer

2x^2 - 5x - 2

Answer

2x^2 + x - 2

Answer

x^2 - 5x + 8

Question 4

Solve for x: x^2 - 5x + 6 = 0

Accepted Answer

x = 2, x = 3

Answer

x = -2, x = 3

Answer

x = 2, x = -3

Answer

x = -2, x = -3

Question 5

Find the roots of the polynomial: x^3 - 2x^2 - 5x + 6

Accepted Answer

x = 1, x = 2, x = 3

Answer

x = -1, x = 2, x = 3

Answer

x = 1, x = -2, x = 3

Answer

x = -1, x = -2, x = 3

Question 6

The polynomial f(x) = x^3 - 3x^2 + kx + 4 has a factor of (x - 2). What is the value of k?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 7

A farmer has 100 feet of fencing to enclose a rectangular plot of land. If the width of the plot is x feet, what is the area of the plot?

Accepted Answer

A = 2x(50 - x)

Answer

A = 100x

Answer

A = (50 - x)^2

Question 8

Factor the quadratic polynomial: x^2 + 5x + 6.

Accepted Answer

(x + 2)(x + 3)

Answer

(x - 2)(x - 3)

Answer

(x + 1)(x + 6)

Answer

(x - 1)(x - 6)

Question 9

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

Accepted Answer

x^2 + x - 6

Answer

x^2 - x - 6

Answer

x^2 + 5x - 6

Answer

x^2 - 5x - 6

Question 10

Which factoring technique is used to factor the polynomial x^2 - 9?

Accepted Answer

Difference of squares

Answer

Trinomial factoring

Answer

Prime factorization

Answer

Sum and product of roots

Question 11

Apply your knowledge of factoring to solve the equation: x^2 - 16 = 0

Accepted Answer

x = ±4

Answer

x = ±8

Answer

x = ±2

Answer

The equation has no real solutions

Question 12

Which of the following polynomials has three terms?

Accepted Answer

Trinomial

Answer

Monomial

Answer

Binomial

Answer

Quadratic

Question 13

Sum the polynomials: (2x^2 - 3x + 1) + (x^2 + 2x - 4).

Accepted Answer

3x^2 + x - 3

Answer

3x^2 - x - 3

Answer

2x^2 + 5x - 3

Answer

2x^2 - x - 3

Question 14

Identify a factor of the polynomial x^3 - 8.

Accepted Answer

x - 2

Answer

x + 2

Answer

x + 4

Answer

x - 4

Question 15

Divide the polynomial x^4 - 16 by x - 2.

Accepted Answer

x^3 + 2x^2 + 4x + 8

Answer

x^3 - 2x^2 + 4x - 8

Answer

x^3 + 2x^2 - 4x - 8

Answer

x^3 - 2x^2 - 4x - 8

Question 16

Evaluate the polynomial (2x^2 - 3x + 1) at x = 2.

Accepted Answer

5

Answer

1

Answer

3

Answer

7

Question 17

Which of the following is NOT a factor of the polynomial x^3 - 8?

Accepted Answer

x^2 + 4

Answer

x - 2

Answer

x + 2

Answer

x - 4

Question 18

The leading coefficient of the polynomial 3x^4 - 2x^3 + 5x^2 - 7x + 1 is:

Accepted Answer

3

Answer

1

Answer

5

Answer

7

Question 19

Which of the following is a polynomial?

Accepted Answer

x^2 + 3x - 5

Answer

x^2 + 3x^-1 - 5

Answer

x + sqrt(x)

Answer

1/(x + 1)

Question 20

Which of the following is the standard form of a polynomial?

Accepted Answer

Terms arranged in descending order of exponents

Answer

Variables listed alphabetically

Answer

Leading coefficient at the beginning

Answer

Constant terms at the end

Question 21

Factor the polynomial: x^2 - 25

Accepted Answer

(x + 5)(x - 5)

Answer

Cannot be factored

Answer

(x + 5)^2

Answer

(x - 5)^2

Question 22

Which of the following polynomials has a degree of 3?

Accepted Answer

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

Answer

3x^2 - 5x + 3

Answer

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

Answer

x^4 - 3x^3 + 2x

Question 23

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

Accepted Answer

x^6/y^6

Answer

x^6/y^2

Answer

y^6/x^6

Answer

x^3/y

Question 24

Which of the following is a monomial polynomial?

Accepted Answer

5x

Answer

(x + 2)(x - 2)

Answer

2x^2 + 3x - 5

Answer

-x^2 + 5x - 7

Question 25

Subtract (2x^2 - 5x + 4) from (3x^2 + 2x - 7)

Accepted Answer

x^2 + 7x - 11

Answer

x^2 - 7x + 11

Answer

x^2 - 3x + 11

Answer

-x^2 + 3x - 11

Question 26

Factor the polynomial expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

Cannot be factored

Answer

(x - 3)^2

Answer

(x + 9)(x - 9)

Question 27

Which of the following expressions is a polynomial?

Accepted Answer

x^2 + 2x - 1

Answer

2/x

Answer

sin(x)

Answer

e^x

Question 28

Factor the polynomial: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)(x + 4)

Answer

(x - 1)(x + 1)

Answer

(x - 2)(x - 2)

Question 29

What is the degree of the polynomial: 2x^4 - 5x^3 + 3x^2 - 7x + 1?

Accepted Answer

4

Answer

6

Answer

3

Answer

5

Question 30

What is the leading coefficient of the polynomial: -3x^5 + 2x^3 - 7x + 1?

Accepted Answer

-3

Answer

-7

Answer

1

Answer

2

Question 31

Which of the following expressions is a polynomial?

Accepted Answer

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

Answer

x - 1/x

Answer

sin(x) + cos(x)

Answer

√x + 5

Question 32

Factor the following polynomial: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

This polynomial cannot be factored.

Answer

(x - 4)(x + 4)

Answer

(x - 1)(x + 4)

Question 33

Which of the following is a polynomial in x?

Accepted Answer

x^2 + 2x - 3

Answer

√x + 1

Answer

log(x) + 1

Answer

1/x + 2

Question 34

Find the sum of the polynomials: (2x^2 - 3x + 1) and (x^2 + 5x - 2)

Accepted Answer

3x^2 + 2x - 1

Answer

3x^2 - 2x + 1

Answer

4x^2 + 2x - 1

Answer

4x^2 - 2x - 1

Question 35

Which of the following polynomials has a leading coefficient of 1?

Accepted Answer

x³ - 2x² + 3x - 4

Answer

2x³ - 4x² + 6x - 8

Answer

3x³ - 6x² + 9x - 12

Question 36

Which of the following is a polynomial with a degree of 3?

Accepted Answer

2x³ + 5x² - 7

Answer

5x + 1

Answer

4x² - 9

Answer

x⁴ + 3x - 2

Question 37

Simplify the expression: (3x² + 2x - 1) + (x² - 4x + 5)

Accepted Answer

4x² - 2x + 4

Answer

2x² - 2x + 4

Answer

4x² + 6x + 4

Question 38

Factor the polynomial: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 1)

Answer

(x - 9)(x - 1)

Question 39

The area of a rectangular garden is represented by the polynomial x² + 7x + 12. What are the dimensions of the garden?

Accepted Answer

(x + 3) and (x + 4)

Answer

(x + 1) and (x + 12)

Answer

(x + 1) and (x + 6)

Answer

(x + 2) and (x + 6)

Question 40

Which of the following is NOT a polynomial?

Accepted Answer

2x^2 + 1/x

Answer

-x^4 + 9

Answer

4x^2 - 7x + 1

Answer

3x^3 - 2x + 5

Question 41

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

Accepted Answer

3

Answer

2

Answer

4

Answer

1

Question 42

Simplify the expression (3x^2 + 2x - 5) + (x^2 - 4x + 1).

Accepted Answer

4x^2 - 2x - 4

Answer

2x^2 - 2x - 4

Answer

2x^2 + 6x - 4

Answer

4x^2 + 6x - 6

Question 43

What is the product of (2x + 3) and (x - 1)?

Accepted Answer

2x^2 + x - 3

Answer

2x^2 + 5x - 3

Answer

2x^2 - 3

Answer

2x^2 - 5x - 3

Question 44

Factor the polynomial 4x^2 - 9.

Accepted Answer

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

Answer

(2x + 9)(2x - 1)

Answer

(4x + 3)(x - 3)

Question 45

Which of the following is a factor of the polynomial x^2 - 5x + 6?

Accepted Answer

(x - 2)

Answer

(x + 3)

Answer

(x + 2)

Answer

(x - 3)

Question 46

The area of a rectangular garden is given by the expression 3x^2 + 5x - 2. If the length of the garden is (3x - 1), what is its width?

Accepted Answer

(x + 2)

Answer

(x - 2)

Answer

(3x - 2)

Answer

(3x + 2)

Question 47

What is the value of the polynomial 2x^3 - 4x^2 + 3x - 1 when x = 2?

Accepted Answer

9

Answer

15

Answer

7

Answer

1

Question 48

Which of the following is the simplified form of (x^2 + 2x - 3) / (x - 1)?

Accepted Answer

x + 3

Answer

x + 1

Answer

x - 3

Answer

x^2 + 1

Question 49

The length of a rectangle is represented by the polynomial 2x + 5 and the width by x - 3. What is the perimeter of the rectangle?

Accepted Answer

6x + 4

Answer

6x - 4

Answer

3x + 2

Answer

2x^2 - x - 15