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Polynomial Equations and Operations Quiz

#1

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

2
Explanation

The degree is the highest power of the variable in the polynomial.

#2

Which of the following is a binomial?

2x - 1
Explanation

A binomial is a polynomial with two terms.

#3

What is the leading coefficient of the polynomial 4x^3 + 2x^2 - 5x + 1?

4
Explanation

It's the coefficient of the term with the highest power of x.

#4

Which of the following is a trinomial?

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

A trinomial is a polynomial with three terms.

#5

What is the constant term of the polynomial 2x^3 - 3x^2 + 4x - 5?

-5
Explanation

It's the term without any x, i.e., the term with x^0.

#6

Which of the following is a monomial?

5x
Explanation

A monomial is a polynomial with only one term.

#7

What is the leading term of the polynomial 6x^5 - 3x^3 + 2x^2 - 4x + 1?

6x^5
Explanation

It's the term with the highest degree.

#8

What is the result of dividing (x^3 - 6x^2 + 11x - 6) by (x - 3)?

x^2 - 3x + 2
Explanation

This is the result obtained using polynomial long division.

#9

What is the sum of all the roots of the polynomial x^3 - 5x^2 + 6x?

5
Explanation

It's determined by Vieta's formulas for cubic equations.

#10

What is the result of dividing (2x^4 - 7x^3 + 3x^2 - 5x + 4) by (x - 2)?

2x^3 - 11x^2 + 20x - 36
Explanation

Result of polynomial division using synthetic division or long division.

#11

What is the sum of all the roots of the polynomial 2x^4 - 3x^3 + 5x^2 - 7x + 1?

-3
Explanation

Determined by Vieta's formulas for quartic equations.

#12

What is the result of dividing (3x^4 + 2x^3 - 5x^2 + 7x - 1) by (x - 1)?

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

Obtained through polynomial division.

#13

What is the sum of all the roots of the polynomial x^4 - 3x^3 + 2x^2 - 5x + 1?

-3
Explanation

Found using Vieta's formulas.

#14

What is the result of dividing (4x^5 + 3x^4 - 2x^3 + x^2 - 5x + 1) by (x - 2)?

4x^4 + 11x^3 + 19x^2 + 39x + 41
Explanation

Result obtained through polynomial long division.

#15

What is the remainder when x^4 + 3x^3 - 4x^2 + 2x - 7 is divided by x - 1?

7
Explanation

The remainder is found using polynomial division.

#16

What is the remainder when x^5 + 2x^4 - 3x^3 + 4x^2 - 5x + 6 is divided by x - 2?

12
Explanation

Calculated using polynomial long division.

#17

What is the remainder when x^6 - 5x^5 + 4x^4 - 3x^3 + 2x^2 - x + 1 is divided by x - 1?

7
Explanation

Calculated using polynomial long division or synthetic division.

#18

What is the remainder when x^7 + 2x^6 - 3x^5 + 4x^4 - 5x^3 + 6x^2 - 7x + 8 is divided by x - 1?

13
Explanation

Calculated using polynomial long division or synthetic division.

#19

What is the remainder when x^8 - 4x^7 + 2x^6 - 3x^5 + 5x^4 - 2x^3 + 4x^2 - 3x + 1 is divided by x - 1?

5
Explanation

Calculated using polynomial long division or synthetic division.

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