Polynomials: Operations, Factoring, and Remainder Theorem

Question 1

Find the remainder when the polynomial x^3 - 2x^2 + 5x - 3 is divided by (x - 1).

Accepted Answer

1

Answer

0

Answer

-1

Answer

-3

Question 2

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

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 3

Expand the polynomial (x + y)^2.

Accepted Answer

x^2 + 2xy + y^2

Answer

x^2 - 2xy + y^2

Answer

x^2 + y^2

Answer

2x^2 + 2xy + y^2

Question 4

Simplify the polynomial (x - 1)^4 - (x + 1)^4.

Accepted Answer

8x^4 - 8x^2

Answer

-8x^4 + 8x^2

Answer

8x^3 - 8x

Answer

-8x^3 + 8x

Question 5

Which of the following is a binomial polynomial?

Accepted Answer

x^2 + 2x + 1

Answer

(x + 1)(x - 2)

Answer

x^3 - 8

Answer

2x^4 - 3x^2 + 5

Question 6

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

Accepted Answer

2, -5, 3, -1

Answer

3, -5, 2, -1

Answer

-1, 3, -5, 2

Answer

1, -2, 3, -5

Question 7

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

Accepted Answer

4

Answer

1

Answer

3

Answer

2

Question 8

Evaluate f(-2) if f(x) = x^3 + 2x - 1.

Accepted Answer

-9

Answer

1

Answer

9

Answer

-1

Question 9

Which polynomial represents a quadratic trinomial?

Accepted Answer

2x^2 + 3x - 1

Answer

x^4 + x^2 + 1

Answer

5x - 2

Answer

x^3 + 2x - 1

Question 10

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

Accepted Answer

4

Answer

1

Answer

2

Answer

-3

Question 11

Simplify the expression: (2x + 1)^2.

Accepted Answer

4x^2 + 4x + 1

Answer

4x^2 + 2x + 1

Answer

2x^2 + 1

Answer

4x^2 + 1

Question 12

Simplify the following polynomial: (x^2 - 3x + 5) - (2x^2 - x + 7)

Accepted Answer

-x^2 - 2x - 2

Answer

x^2 + 2x + 12

Answer

x^2 - 4x + 2

Answer

-x^2 - 4x + 12

Question 13

Multiply the following polynomials: (2x - 5)(x + 3)

Accepted Answer

2x^2 - x - 15

Answer

2x^2 + x - 15

Answer

2x^2 + x + 15

Answer

2x^2 - x + 15

Question 14

Which of the following is a monomial?

Accepted Answer

5x^2

Answer

x^2 - xy

Answer

x + y

Question 15

Which of the following is a binomial?

Accepted Answer

x^2 + 2x

Answer

x^3 + 2x^2 - 1

Answer

x^3

Answer

x

Question 16

Which of the following is a cubic polynomial?

Accepted Answer

x^3 - 2x + 1

Answer

x^2 + x - 5

Answer

x

Question 17

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

Accepted Answer

4

Answer

2

Answer

3

Answer

1

Question 18

If P(x) = x² - 3x + 2 and Q(x) = 2x - 1, what is P(x) + Q(x)?

Accepted Answer

x² - x + 1

Answer

x² - 5x + 1

Answer

3x² - 3x + 1

Question 19

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

Accepted Answer

x² + x - 6

Answer

x² - x - 6

Answer

x² - 5x - 6

Answer

x² + 5x - 6

Question 20

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

Accepted Answer

5

Answer

-1

Answer

-3

Answer

1

Question 21

Factor the polynomial: x² - 4x - 12

Accepted Answer

(x - 6)(x + 2)

Answer

(x + 6)(x - 2)

Answer

(x - 4)(x + 3)

Question 22

Which of the following is a factor of the polynomial x³ - 8 ?

Accepted Answer

x - 2

Answer

x + 2

Answer

x + 4

Answer

x - 4

Question 23

Find the quotient when (2x³ - 5x + 1) is divided by (x - 1).

Accepted Answer

2x² + 2x - 3

Answer

2x² + 2x + 3

Answer

2x² - 2x - 3

Question 24

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

Accepted Answer

x² + 3x - 10 square meters

Answer

x² - 7x - 10 square meters

Answer

x² + 7x - 10 square meters

Answer

x² - 3x - 10 square meters

Question 25

If (x - 3) is a factor of a polynomial P(x), what is the value of P(3)?

Accepted Answer

0

Answer

Cannot be determined

Answer

3

Answer

-3

Question 26

The concentration of a drug in the bloodstream t hours after administration is given by C(t) = -t³ + 4t² + 2t. What is the concentration after 2 hours?

Accepted Answer

12

Answer

4

Answer

8

Answer

16