8th Grade Math: Factoring & Inequalities Challenge

1. Sarah has 3x + 5x - 2. What is the simplified expression?

• 8x + 2

• 5x - 2

• 3x + 2

• 8x - 2

2. If the area of a square is represented by x^2 + 4x + 4, what is the length of one side?

• x + 3

• x + 2

• x + 4

• x + 1

3. A rectangle has a length of (2x + 3) and a width of (x - 1). Write an expression for the area and factor it.

• (2x - 3)(x + 1)

• (2x + 3)(x - 1)

• (2x - 1)(x + 3)

• (2x + 1)(x + 3)

4. The sum of two numbers is greater than 15. If one number is x, write an inequality for the other number.

• y < 15 - x

• y > 15 - x

• y >= 15 - x

• y = 15 - x

5. If 4√x = 16, what is the value of x?

• 16

• 32

• 4

• 8

6. A store sells pencils for $0.50 each and erasers for $0.75 each. If you buy x pencils and y erasers, write an expression for the total cost and simplify it.

• 0.25x + 0.50y

• 0.75x + 0.50y

• 0.50x + 1.00y

• 0.50x + 0.75y

7. The perimeter of a triangle is represented by the expression 2x + 3y + 5. If the perimeter is less than 20, write an inequality.

• 2x + 3y + 5 > 20

• 2x + 3y + 5 ≤ 20

• 2x + 3y + 5 < 20

• 2x + 3y + 5 = 20

8. Factor the polynomial x^2 - 9. What are the factors?

• (x - 3)(x + 3)

• (x - 6)(x + 6)

• (x - 1)(x + 1)

• (x - 9)(x + 9)

9. If the height of a triangle is represented by 3√x and the base is 2√x, what is the area of the triangle?

• 4x

• 3x

• 6√x

• 1.5x

10. A car rental company charges a flat fee of $20 plus $0.15 per mile driven. Write an inequality to represent the total cost if you want to spend less than $50.

• 20 + 0.15m < 50

• 20 + 0.15m = 50

• 20 + 0.15m > 50

• 0.15m < 30