Master Polynomials in Algebra II: Interactive Quizzes and Practice

Question 1

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

Accepted Answer

4

Answer

1

Answer

2

Answer

5

Question 2

Identify the leading coefficient of the polynomial f(x) = 2x^3 - 5x^2 + 7x - 1.

Accepted Answer

2

Answer

-5

Answer

7

Answer

-1

Question 3

What's the degree of the polynomial p(x) = x³ - 2x² + 5x - 1?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 4

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

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 5

What is the degree of the polynomial f(x) = x³ - 2x² + 5?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 6

In the polynomial P(x) = 3x³ - 2x² + 5x - 7, what is the coefficient of the x-term?

Accepted Answer

5

Answer

3

Answer

-2

Question 7

A polynomial has a root at x = 3. Which expression must be a factor of this polynomial?

Accepted Answer

x - 3

Answer

x + 3

Answer

x² + 3x + 9

Answer

x² - 9x + 9

Question 8

Which method is most efficient for factoring the polynomial x^4 - 16?

Accepted Answer

Using the difference of squares formula

Answer

Factoring by grouping

Answer

Factoring by completing the square

Answer

Using synthetic division

Question 9

In a polynomial expression, what is the term for the numerical value that does not have any variables?

Accepted Answer

Constant term

Answer

Coefficient

Answer

Degree

Answer

Variable

Question 10

Find the degree of the polynomial: P(x) = 5x^4 - 2x^3 + 6x^2 - 8x + 1.

Accepted Answer

4

Answer

2

Answer

5

Question 11

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

Accepted Answer

4

Answer

3

Answer

5

Answer

6

Question 12

Identify the leading coefficient of the polynomial 3x^4 - 2x^3 + x^2 - x + 5.

Accepted Answer

3

Answer

-2

Answer

1

Answer

-1

Question 13

Analyze the polynomial function f(x) = 3x^4 - 5x^2 + 2x - 1. Determine its degree, leading coefficient, and constant term.

Accepted Answer

Degree: 4, Leading Coefficient: 3, Constant Term: -1

Answer

Degree: 3, Leading Coefficient: -5, Constant Term: 1

Answer

Degree: 2, Leading Coefficient: 2, Constant Term: -5

Question 14

Factor the polynomial: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x + 9)(x - 9)

Answer

Cannot be factored

Question 15

Which of the following is not a type of polynomial function?

Accepted Answer

Exponential function

Answer

Linear function

Answer

Quadratic function

Answer

Cubic function

Question 16

Simplify the expression: (3x + 2) / (x - 1)

Accepted Answer

3x + 1

Answer

3 + 2 / (x - 1)

Answer

3x - 1

Answer

Cannot be simplified

Question 17

Identify the degree of the polynomial: 3x⁴ - 2x² + 5

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 18

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

Accepted Answer

4

Answer

3

Answer

5

Answer

1

Question 19

Factor the quadratic polynomial x^2 - 9:

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x + 9)

Answer

(x - 3)^2

Answer

(x + 9)(x - 9)

Question 20

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

Accepted Answer

4

Answer

3

Answer

2

Question 21

Solve the polynomial equation x^2 - 4 = 0. Express the solutions in the form of x = ...

Accepted Answer

x = ±2

Answer

x = 0, 4

Answer

x = 2, -4

Answer

x = ±4

Question 22

Identify the polynomial with the highest degree from the given options.

Accepted Answer

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

Answer

2x^3 - 3x^2 + x

Answer

4x^2 - 3x + 2

Answer

5x - 4

Question 23

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

Accepted Answer

x - 2

Answer

x^2 - 2x + 4

Answer

x^2 + 2x + 4

Answer

x + 2

Question 24

Find the end behavior of the polynomial P(x) = -x⁴ + 2x³ - x² + 3

Accepted Answer

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

Answer

As x approaches infinity and negative infinity, P(x) approaches infinity

Question 25

Simplify: (2x² - 3x + 4) ÷ (x - 1)

Accepted Answer

2x - 1

Answer

(2x - 1)(x - 1)

Answer

2x² - x - 4

Answer

Cannot be simplified

Question 26

What is the term used to describe the highest exponent of the variable in a polynomial expression?

Accepted Answer

Degree

Answer

Coefficient

Answer

Exponent

Answer

Constant

Question 27

Which of the following polynomials has a degree of 4?

Accepted Answer

5x⁴ - 2x³ + 7x² - 1

Answer

x² - 4x + 5

Answer

3x³ - 2x² + 7x - 1

Answer

2x + 3

Question 28

What is the result of adding the polynomials (3x² + 2x - 1) and (x² - 4x + 5)?

Accepted Answer

4x² - 2x + 4

Answer

4x² - 6x + 4

Answer

2x² - 2x + 4

Answer

4x² + 6x + 4

Question 29

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

Accepted Answer

2x² - x - 6

Answer

2x² - 7x - 6

Answer

2x² + 7x - 6

Answer

2x² + x - 6

Question 30

Which of the following is a factor of the polynomial x² - 5x + 6?

Accepted Answer

(x - 2)

Answer

(x - 3)

Answer

(x + 2)

Answer

(x + 3)

Question 31

What is the quotient when x³ + 2x² - 5x - 6 is divided by x + 2?

Accepted Answer

x² - 5

Answer

x² + 2x - 5

Answer

x² + 5

Answer

x² - 2x - 5

Question 32

What are the roots of the polynomial equation x² - 7x + 12 = 0?

Accepted Answer

x = 3, x = 4

Answer

x = 3, x = -4

Answer

x = -3, x = 4

Answer

x = -3, x = -4

Question 33

What is the remainder when x³ - 3x² + 2x - 1 is divided by x - 1?

Accepted Answer

-1

Answer

1

Answer

2

Answer

0

Question 34

Which of the following is a possible rational root of the polynomial equation 2x³ - 5x² + 3x - 1 = 0?

Accepted Answer

1/2

Answer

2

Answer

-1

Question 35

What is the simplified form of (x² + 2x - 3) / (x - 1)?

Accepted Answer

x + 3

Answer

x² - 1

Answer

x - 3

Answer

x² + 1

Question 36

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

Accepted Answer

3

Answer

4

Answer

2

Answer

1

Question 37

Simplify: (3x^2 + 2x - 1) + (x^2 - 5x + 4)

Accepted Answer

4x^2 - 3x + 3

Answer

2x^2 - 3x + 3

Answer

2x^2 + 7x + 3

Answer

4x^2 + 7x + 3

Question 38

Multiply: (2x + 3)(x - 2)

Accepted Answer

2x^2 - x - 6

Answer

2x^2 - 7x - 6

Answer

2x^2 + x - 6

Answer

2x^2 + 7x - 6

Question 39

Divide: (x^3 - 2x^2 + 5x - 1) ÷ (x - 1)

Accepted Answer

x^2 - x + 4 + 3/(x - 1)

Answer

x^2 - x + 4 - 3/(x - 1)

Answer

x^2 + x + 4 + 3/(x - 1)

Answer

x^2 + x + 4 - 3/(x - 1)

Question 40

Factor the polynomial: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x - 3)

Answer

(x + 3)(x + 3)

Question 41

Factor completely: 2x^3 - 8x

Accepted Answer

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

Answer

2x(x^2 - 4)

Answer

2x(x - 2)^2

Answer

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

Question 42

Find the roots of the polynomial equation: x^2 - 5x + 6 = 0

Accepted Answer

x = 2, x = 3

Answer

x = -2, x = -3

Answer

x = -1, x = -6

Answer

x = 1, x = 6

Question 43

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

Accepted Answer

x - 2

Answer

x + 1

Answer

x + 2

Answer

x - 1

Question 44

The polynomial 2x^2 + 5x - 3 represents the area of a rectangle. What is the length of the rectangle if the width is (x + 3)?

Accepted Answer

2x - 1

Answer

x + 1

Answer

2x + 1

Answer

x - 1

Question 45

The graph of a polynomial function intersects the x-axis at the points (-2, 0), (1, 0), and (3, 0). What is the degree of the polynomial function?

Accepted Answer

At least 3

Answer

Exactly 2

Answer

At least 4

Answer

Exactly 1