Polynomials & Zeros: An 8th Grade Algebra Challenge

1. A gardener has a rectangular garden with a length of 3√2 meters and a width of 2√2 meters. What is the area of the garden in square meters?

• 12 square meters

• 6 square meters

• 10 square meters

• 8 square meters

2. If 5x + 3 = 2x + 12, what is the value of x?

• 1

• 3

• 10

• 5

3. The sum of two numbers is 20, and their difference is 4. What are the two numbers?

• 15 and 5

• 10 and 10

• 18 and 2

• 12 and 8

4. Factor the polynomial x² - 9 completely. What are the factors?

• (x - 3)(x + 3)

• (x - 1)(x + 1)

• (x - 9)(x + 9)

• (x - 3)(x - 3)

5. A car travels at a speed of 60 km/h. How long will it take to travel a distance of 240 km? Rearrange the formula d = rt to find time.

• 4 hours

• 6 hours

• 2 hours

• 3 hours

6. If the expression 2√(x + 3) = 8, what is the value of x?

• 5

• 13

• 0

• 10

7. A rectangle has a perimeter of 50 meters. If the length is 5 meters more than the width, what are the dimensions of the rectangle?

• Width: 8 meters, Length: 13 meters

• Width: 5 meters, Length: 10 meters

• Width: 12 meters, Length: 17 meters

• Width: 10 meters, Length: 15 meters

8. Solve the inequality 3x - 7 < 2. What is the solution set?

• x > 3

• x = 3

• x ≤ 3

• x < 3

9. Find the zeros of the polynomial p(x) = x² - 5x + 6. What are the zeros?

• 1 and 4

• The zeros are 2 and 3.

• 0 and 6

• -2 and -3

10. Rearrange the formula A = lw to solve for l in terms of A and w. What is the new formula?

• l = A - w

• l = A + w

• l = A/w

• l = A * w