Master Polynomials: Operations, Properties, and Applications

Question 1

Which term is NOT part of the polynomial 3x^2 - 5x + 2?

Accepted Answer

2x

Answer

3x^2

Answer

-5x

Answer

2

Question 2

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

Accepted Answer

-3

Answer

5

Answer

-2

Answer

2

Question 3

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

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 4

Divide the polynomial 2x^3 - 4x^2 + 6x - 8 by x - 2:

Accepted Answer

2x^2 + 2x - 2

Answer

2x^2 - 2x + 2

Answer

2x^2 - 4x + 2

Answer

2x^2 + 4x - 2

Question 5

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

Accepted Answer

5, -2, 3, -1

Answer

-2, 3, -1, 5

Answer

3, -1, 5, -2

Answer

-1, 5, -2, 3

Question 6

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

Accepted Answer

3x^2 + 8x - 1

Answer

3x^2 + 2x - 1

Answer

3x^2 - 8x - 1

Answer

3x^2 - 2x - 1

Question 7

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

Accepted Answer

9x^2 - 4

Answer

9x^2 + 4

Answer

9x^2 - 12x + 4

Answer

9x^2 + 12x + 4

Question 8

Find the difference between the polynomials (x^3 - 2x^2 + 3x - 1) and (2x^3 + x^2 - 5x + 2):

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 9

Which of the following is the leading coefficient of the polynomial 4x^5 - 2x^3 + 6:

Accepted Answer

4

Answer

5

Answer

6

Answer

2

Question 10

Which of the following expressions represents a polynomial?

Accepted Answer

x³ + 2x - 5

Answer

1/(x-1)

Answer

cos(x)

Answer

√x

Question 11

Determine the degree of the polynomial 3x⁴ - 2x² + 5.

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 12

Determine the zeros of the polynomial 2x² + 5x - 3.

Accepted Answer

x = -1/2, x = 3

Answer

x = -3/2, x = -1

Answer

x = 1/2, x = -3

Answer

x = 3/2, x = 1

Question 13

In a polynomial, which term has the highest degree and the coefficient in front of it is called the?

Accepted Answer

Leading coefficient

Answer

Constant term

Answer

Variable with the highest degree

Question 14

Which property is NOT shared by polynomials?

Accepted Answer

Closure under division

Answer

Closure under addition

Answer

Closure under subtraction

Answer

Closure under multiplication

Question 15

Simplify the polynomial: (2x² + 3x - 5) + (4x² - 6x + 2)

Accepted Answer

6x² - 9x + 7

Answer

6x⁴ - 3x² - 3

Answer

6x² - 3x - 3

Answer

This polynomial cannot be simplified further.

Question 16

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

Accepted Answer

3

Answer

2

Answer

5

Answer

-1

Question 17

Perform long division to find the quotient when (x^3 - 2x^2 + 5x - 6) is divided by (x - 2).

Accepted Answer

x^2 + 4x - 3

Answer

x^2 - 4x + 3

Answer

x^2 - 2x + 3

Answer

x^2 + 2x + 3

Question 18

Which of these is an example of a polynomial function?

Accepted Answer

y = 2x^2 - 3x + 1

Answer

y = 1/x

Answer

y = sin(x)

Answer

y = log(x)

Question 19

Find the leading coefficient of the polynomial 5x^3 - 2x^2 + 7.

Accepted Answer

5

Answer

2

Answer

7

Answer

None of the provided values

Question 20

Identify the constant term of the polynomial 3x^4 - 5x^2 + 2.

Accepted Answer

2

Answer

0

Answer

3

Answer

5

Question 21

Which of the provided factors is NOT a factor of the polynomial x^3 - 2x^2 + x?

Accepted Answer

x - 2

Answer

x

Answer

x - 1

Answer

x + 1

Question 22

When (x^3 - 2x^2 + 5x - 1) is divided by (x - 1), what is the quotient?

Accepted Answer

x^2 - x + 4

Answer

x^2 + x + 5

Answer

x^2 + x - 4

Answer

x^2 - x - 5

Question 23

Find the zeros of the polynomial p(x) = x^2 - 5x + 6.

Accepted Answer

2, 3

Answer

-2, -3

Answer

1, -6

Answer

3, -2

Question 24

Which statement below is NOT a property of polynomials?

Accepted Answer

The degree of a polynomial can be a negative integer

Answer

Polynomials are closed under addition and subtraction

Answer

Polynomials are closed under multiplication

Answer

Polynomials can have rational coefficients

Question 25

Find the degree of the polynomial resulting from the multiplication of (x - 2) and (x^2 + 3x - 1).

Accepted Answer

5

Answer

2

Answer

3

Answer

4

Question 26

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

Accepted Answer

2

Answer

-5

Answer

7

Answer

1

Question 27

Determine the constant term of the polynomial f(x) = 3x^4 - 2x^2 + 5.

Accepted Answer

5

Answer

3

Answer

-2

Answer

0

Question 28

Which of the following expressions qualifies as a trinomial?

Accepted Answer

x^2 + 2x + 1

Answer

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

Answer

x^4 - x^2 + 1

Answer

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

Question 29

Calculate the sum of the polynomials (x^2 + 2x + 3) and (2x^2 - x + 1).

Accepted Answer

3x^2 + 3x + 4

Answer

x^2 + x + 2

Answer

3x^2 + x + 4

Answer

4x^2 + x + 4

Question 30

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

Accepted Answer

x^2 + x - 6

Answer

x^2 - x - 6

Answer

x^2 - 5x - 6

Answer

x^2 + 5x - 6

Question 31

Which of the following is a factor of the polynomial x^2 - 4?

Accepted Answer

x - 2

Answer

x + 2

Answer

x^2 + 2x + 4

Answer

x^2 - 2x + 4

Question 32

Identify the graph that best represents the polynomial function f(x) = -x^2 + 4x - 3.

Accepted Answer

A parabola opening downwards

Answer

A parabola opening upwards

Answer

A straight line

Answer

A circle

Question 33

Which of the following polynomials is of the third degree?

Accepted Answer

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

Answer

x + 2

Answer

x^2 - 3x + 1

Answer

x^4 - x^2 + 1

Question 34

Which of the following is not a defining property of polynomials?

Accepted Answer

Polynomials are discontinuous functions.

Answer

Polynomials can be added and subtracted.

Answer

Polynomials can be multiplied.

Answer

Polynomials can be factored into linear factors.

Question 35

Identify the polynomial that has a positive leading coefficient and an odd degree.

Accepted Answer

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

Answer

x^2 - 3x + 2

Answer

2x^2 + x - 3

Answer

-x^3 + 4x^2 - 5x + 1

Question 36

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

Accepted Answer

5/2

Answer

3/2

Answer

-5/2

Answer

-3/2

Question 37

A rectangular garden has a length of (x + 3) meters and a width of x meters. Which of the following expressions represents the area of the garden?

Accepted Answer

x^2 + 6x + 3

Answer

x^2 + 3x

Answer

2x + 3

Answer

2x^2 + 3x

Question 38

Which of the following is NOT a characteristic of polynomials?

Accepted Answer

They are continuous functions

Answer

They are composed of terms

Answer

Their variables have non-negative integer exponents

Answer

They can be simplified using algebraic operations

Question 39

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 40

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

Accepted Answer

x - 2

Answer

x + 2

Answer

x^2 - 2

Answer

x^2 + 2

Question 41

Solve the polynomial equation 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 42

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

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 43

Which of the following is a polynomial function?

Accepted Answer

f(x) = x^2 + 2x

Answer

f(x) = |x|

Answer

f(x) = sin(x)

Answer

f(x) = e^x

Question 44

Find the quotient when dividing f(x) = x^4 - 3x^2 + 2x - 1 by x^2 - 1.

Accepted Answer

x^2 + 2

Answer

x^2 - 2

Answer

x^2 + 3x + 2

Answer

x^2 - 3x + 2

Question 45

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

Accepted Answer

5

Answer

3

Answer

4

Answer

6

Question 46

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

Accepted Answer

-2

Answer

2

Answer

5

Answer

3

Question 47

Find the constant term in the polynomial: 2x^4 - 3x^3 + 2x - 5.

Accepted Answer

-5

Answer

2

Answer

-3

Answer

5

Question 48

Which of the following expressions is a polynomial?

Accepted Answer

2x³ + 5x² - 7x + 1

Answer

x / (x + 1)

Answer

√x + 2

Question 49

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

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 50

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

Accepted Answer

3x² + x - 4

Answer

x² + x - 4

Answer

2x² + 5x - 4

Answer

3x² - x - 6

Question 51

Factor the polynomial: x² - 5x + 6

Accepted Answer

(x - 2)(x - 3)

Answer

(x - 2)(x + 6)

Answer

(x + 2)(x + 3)

Answer

(x + 2)(x - 6)