Master Polynomials: Operations and Applications in Mathematics Education

Question 1

Find the difference between (2x³ + x² - 5x + 2) and (x³ - 2x² + 3x - 1):

Accepted Answer

x³ + 3x² - 8x + 3

Answer

x³ - 3x² - 8x + 3

Answer

x³ + 3x² + 8x + 3

Answer

x³ - 3x² + 8x + 3

Question 2

Multiply (x - 2) by (x² + 3x - 1):

Accepted Answer

x³ + 5x² - 7x - 2

Answer

x³ - x² - 7x + 2

Answer

x³ + 5x² + 7x + 2

Answer

x³ - x² + 7x - 2

Question 3

Determine the degree of the polynomial: 2x⁴ - 5x³ + 3x² - x + 1

Accepted Answer

4

Answer

3

Answer

5

Answer

6

Question 4

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

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 5

Determine the leading coefficient of the polynomial (2x^4 - 5x^3 + 3x^2 - 2x + 1).

Accepted Answer

2

Answer

1

Answer

3

Answer

5

Question 6

Find the constant term of the polynomial (x^3 - 2x^2 + 5x - 7).

Accepted Answer

-7

Answer

5

Answer

2

Answer

-2

Question 7

Which operation is valid for polynomials?

Accepted Answer

Multiplication

Answer

Differentiation

Answer

Integration

Question 8

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

Accepted Answer

2

Answer

1

Answer

3

Question 9

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 10

Find the remainder when x³ - 2x² + x - 3 is divided by x - 1 using the polynomial remainder theorem.

Accepted Answer

-3

Answer

1

Answer

x - 1

Question 11

What is the shape of the graph of the polynomial f(x) = -x² + 4x - 3?

Accepted Answer

A parabola opening downwards

Answer

A parabola opening upwards

Answer

A straight line

Answer

A circle

Question 12

Determine the degree of the polynomial 5x^3 - 2x^2 + 7x - 1.

Accepted Answer

3

Answer

4

Answer

2

Question 13

Find the result of adding the polynomials (3x^2 + 2x - 1) and (x^2 - 4x + 5).

Accepted Answer

4x^2 - 2x + 4

Answer

2x^2 - 2x + 4

Answer

2x^2 + 6x - 6

Answer

4x^2 + 6x - 6

Question 14

Multiply the polynomials (2x + 1) and (x - 3).

Accepted Answer

2x^2 - 5x - 3

Answer

2x^2 - 5x + 3

Answer

2x^2 + 5x - 3

Question 15

Determine the polynomial representing the quotient of (6x^3 + 11x^2 - 4x - 4) divided by (2x + 1).

Accepted Answer

3x^2 + 4x - 4

Answer

3x^2 - 4x + 4

Answer

3x^2 + 4x + 4

Answer

3x^2 - 4x - 4

Question 16

Simplify the expression (x^2 - 4) / (x - 2).

Accepted Answer

x + 2

Answer

x - 2

Answer

x - 4

Answer

x^2 - 2

Question 17

Identify a factor of the polynomial x^2 - 9.

Accepted Answer

x + 3

Answer

x - 9

Answer

x - 3

Answer

x + 9

Question 18

Consider a rectangular garden with a length of (2x + 3) meters and a width of (x - 1) meters. Calculate the area of the garden in square meters.

Accepted Answer

2x^2 + x - 3

Answer

2x^2 + x + 3

Answer

2x^2 - x - 3

Answer

2x^2 - x + 3

Question 19

The polynomial function f(x) = x^3 - 3x^2 + 2x has a zero at x = 0. Determine the multiplicity of this zero.

Accepted Answer

1

Answer

3

Answer

2

Answer

0

Question 20

Express the polynomial (2x - 1)^2 in its standard form.

Accepted Answer

4x^2 - 4x + 1

Answer

4x^2 + 4x + 1

Answer

4x^2 - 2x + 1

Answer

4x^2 - 1

Question 21

For the polynomial function f(x) = x^4 - 5x^2 + 4, given that x = 1 is a zero, determine another zero of this function.

Accepted Answer

-1

Answer

2

Answer

4

Answer

3

Question 22

Which of the following is the simplified form of (3x² + 5x - 2) - (x² - 2x + 1)?

Accepted Answer

2x² + 7x - 3

Answer

2x² + 3x - 3

Answer

4x² + 3x - 1

Question 23

What is the product of (2x + 3) and (x - 4)?

Accepted Answer

2x² - 5x - 12

Answer

2x² + 5x + 12

Answer

2x² - 5x + 12

Answer

2x² + 5x - 12

Question 24

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

Accepted Answer

x² - 5

Answer

x² - 5x - 6

Answer

x² + 5

Question 25

The degree of the polynomial 4x⁵ - 2x³ + 7 is:

Accepted Answer

5

Answer

3

Answer

7

Question 26

What is the leading coefficient of the polynomial 3x⁴ + 2x² - 5x + 1?

Accepted Answer

3

Answer

1

Answer

2

Answer

-5

Question 27

Which of the following is a polynomial function?

Accepted Answer

f(x) = 2x³ - 5x + 1

Answer

f(x) = 1/x² + 3

Answer

f(x) = √x + 2

Answer

f(x) = 2ˣ - 1

Question 28

The sum of the monomials 5x²y and -3x²y is:

Accepted Answer

2x²y

Answer

-8x²y

Answer

-2x²y

Answer

8x²y

Question 29

What is the value of the polynomial 2x³ - 3x + 1 when x = 2?

Accepted Answer

13

Answer

-13

Answer

1

Answer

-1

Question 30

A rectangular garden has a length of (2x + 3) meters and a width of (x - 1) meters. What is the area of the garden?

Accepted Answer

2x² + x - 3 square meters

Answer

2x² + 3x - 3 square meters

Answer

2x² - x - 3 square meters

Answer

2x² - 3x - 3 square meters

Question 31

The polynomial (x² + 2x - 3) represents the profit of a company in thousands of dollars. What is the profit when x = 5?

Accepted Answer

$32,000

Answer

$22,000

Answer

$42,000

Answer

$12,000