Polynomials

Division and Multiplication

100

What is (5n + 6)(5n - 5)

25n² + 5n - 30 

200

What is (16x⁴ + 20x³ - 12x) / 4x ?

4x³ + 5x² - 3

300

What is the value of (x² + 7x + 12) / (x +3)

x + 4

400

What is the remainder of (x² - x - 29)/ (x - 6) 

1

500

What is the remainder of (11x - 3 + 9x³)/(3x + 2)

-13

Addition and Subtraction

100

What is the value of (2x + 7x + 12) - (5x - 3) 

4x + 15

200

What is the value of 2x² - 4x + (-2x + 3x³ + 1)

3x³ + 2x² - 6x + 1

300

If a triangle has side lengths of x + 2, x² - 4, and 3x - 8 what is its perimeter? 

x² + 4x - 10

400

If an equilateral triangle has side lengths of 2x - 4, what is it's perimeter? 

6x - 12

500

If a triangle has a perimeter of 3x² + 4x - 2 and side lengths of 2x - 1 and 2x² + x, what is the missing side length in terms of x? 

x² - x - 1

Factoring

100

What is the greatest common factor of 3x²y³ + 3xy³?

3xy³

200

What is greatest common factor of (2x²y³z² + 4x²yz⁴ + x³yz²)?

xyz²

300

What are the factors of a² + 7a + 10?

(a + 5)(a + 2) 

400

What are the factors of 5n² + 19n + 12? 

(5n + 4)(n + 3) 

500

What are the factors of 2x² + 3xy - 9y²?

(2x - 3y)(x + 3y)

Rational Expressions

100

Simplify (4x² + 4x)/(16x)

(x + 1)/4

200

Simplify (4x² - 9)\(2x - 3) 

(2x + 3)

300

Simplify (a² + 3a - 28)/(a² - 49) 

(a - 4)/(a - 7) 

400

(3x² + 7x + 2)/(3x² + 13x + 4)

(x + 2)/(x + 4) 

500

(xy - 6x + 2y - 12)/(y² - 6y)

(x + 2)/y 

Solving Equations

100

What are solutions to the equation: 

x² + 4x - 12 = 0

x = -6, 2

200

What are solutions to the equation

x² - x = 56

x = 8, -7

300

What are solutions to the equation

3x² - 2x - 5 = 0

x = 5/3, -1

400

What are solutions to the equation 

9x² + 66x + 21 = 0

x = -7, -1/3

500

What are solutions to the equation

16b² - 100 = -60b

b = 5/4, -5