Polynomial Equations and Factoring Quiz

Test your algebra skills with questions on quadratic equations, factoring, and polynomial properties. Try it now!

#1

Which of the following is a quadratic polynomial?

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

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

4
2
5
3
#3

What is the degree of the polynomial 6x^4 + 3x^3 - 2x^2 + 8?

4
3
2
5
#4

What is the solution to the equation x^2 - 9 = 0?

x = ±3
x = ±2
x = 9
x = -9
#5

What is the factorization of the expression 4x^2 - 25y^2?

(2x + 5y)(2x - 5y)
(4x - 25y)(4x + 25y)
(2x - 5y)(2x + 5y)
(2x)^2 - (5y)^2
#6

Which method is used to find the roots of a quadratic equation?

Factoring
Completing the square
Quadratic formula
All of the above
#7

Factorize the quadratic expression: 2x^2 - 8x + 6

(2x - 3)(x - 2)
(x - 3)(2x - 2)
(2x - 1)(x - 6)
(x - 1)(2x - 6)
#8

If one root of the quadratic equation ax^2 + bx + c = 0 is 3, what is the other root?

-c/a
c/a
-b/a
b/a
#9

What is the sum of the roots of the quadratic equation 2x^2 - 5x + 3 = 0?

-3/2
5/2
3/2
-5/2
#10

Solve the equation x^2 - 4 = 0.

x = 2
x = -2
x = ±2
x = 4
#11

Which method is used to factorize a quadratic trinomial in the form ax^2 + bx + c when 'a' is not equal to 1?

Factoring by grouping
Quadratic formula
Completing the square
Long division
#12

What is the remainder when dividing 4x^3 - 9x^2 + 5x - 7 by (x - 2)?

5
7
-3
0
#13

Which method is used to factorize a cubic polynomial?

Completing the square
Trial and error
Long division
Quadratic formula
#14

What is the product of the roots of the quadratic equation 4x^2 - 7x + 2 = 0?

1/2
2/4
7/4
2
#15

Factorize the following expression: x^3 - 8

(x - 2)^2
(x + 2)(x^2 - 2x + 4)
(x - 2)(x^2 + 2x + 4)
(x + 2)^2
#16

What is the remainder when dividing the polynomial 3x^4 - 7x^3 + 5x^2 - 9x + 2 by (x - 1)?

4
3
-7
-2
#17

Find the value of 'k' for which x + k is a factor of the polynomial 2x^2 - 5x - 3.

1
-1
3
-3

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