8th Grade Challenge: Inequalities & Quadratic Factoring

1. A square garden has an area of 144 square feet. What is the length of one side of the garden? (Use radicals)

• 14

• 12

• 10

• 16

2. If 3x + 5 < 20, what is the range of values for x? (Solve the inequality)

• x < 5

• x = 5

• x < 10

• x > 5

3. Factor the polynomial x^2 + 7x + 10. What are the factors?

• (x + 3)(x + 4)

• (x + 2)(x + 5)

• (x + 1)(x + 10)

• (x - 2)(x - 5)

4. A rectangle's length is 3 feet more than its width. If the area is 40 square feet, find the dimensions of the rectangle. (Set up and solve an equation)

• Width: 3 feet, Length: 6 feet

• Width: 4 feet, Length: 7 feet

• Width: 6 feet, Length: 9 feet

• Width: 5 feet, Length: 8 feet

5. The height of a triangle is represented by h = 2x + 3. If the area of the triangle is 30 square units, find the value of x. (Rearranging formulas)

• 2

• 1.5

• 6

• 4

6. Solve the inequality 2(x - 3) > 4. What values of x satisfy this inequality?

• x ≤ 4

• x = 5

• x < 3

• x > 5

7. A car's value decreases according to the formula V = 20000(1 - 0.15t), where t is the number of years. After how many years will the car's value be less than $10,000? (Create and solve an inequality)

• 4 years

• 8 years

• 6 years

• 2 years

8. Find the zeros of the polynomial p(x) = x^2 - 5x + 6. What are the x-intercepts?

• x = 1, x = 6

• x = 2, x = 3

• x = 0, x = 5

• x = -2, x = -3

9. If 4x^2 - 12x = 0, factor the expression and find the values of x. (Finding zeros)

• x = -3, x = 4

• x = 0, x = 5

• x = 1, x = 2

• x = 0, x = 3

10. A triangle has sides of lengths x, x + 2, and x + 4. If the perimeter is 30, find the value of x. (Set up and solve an equation)

• 6

• 8

• 10

• 12