Solving Polynomial Word Problems for 8th Grade Math

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is represented by the polynomial equation A = x(x + 3), where x is the width, find the dimensions of the garden.

• Width: x - 3 meters, Length: x + 3 meters

• Width: x meters, Length: x + 3 meters

• Width: x + 3 meters, Length: x meters

• Width: x meters, Length: x - 3 meters

The height of a triangular prism is represented by the polynomial h = 2x^2 + 3x - 5. If the base area of the prism is 10 square meters, find the height when x = 1.

• 2

• -3

• 5

• 0

A car's distance from a starting point can be modeled by the polynomial function d(t) = 4t^2 + 2t, where t is time in hours. How far will the car be after 3 hours?

• 42

• 30

• 36

• 50

A toy company produces a polynomial number of toys each month, represented by T(x) = 5x^3 - 2x^2 + 4x. If x represents the number of months, how many toys will they produce in 2 months?

• 20

• 50

• 30

• 40

The profit P from selling x items can be modeled by the polynomial P(x) = -x^2 + 50x - 200. How many items should be sold to maximize profit?

• 30

• 25

• 20

• 40

A farmer has a field shaped like a trapezoid, and its area can be represented by the polynomial A = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the bases and h is the height. If b1 = 10 and b2 = 20, find the height when the area is 150 square meters.

• 10

• 25

• 5

• 15

The volume V of a cylinder can be modeled by the polynomial V = πr^2h. If the radius r is 3 cm and the height h is represented by the polynomial h = 2x + 1, find the volume when x = 2.

• 30π cm³

• 45π cm³

• 15π cm³

• 60π cm³

A local bakery sells cupcakes for a price modeled by the polynomial P(x) = 3x^2 - 12x + 15. What is the price of cupcakes when x = 2?

• 1

• 5

• 3

• 10

A swimming pool's volume can be represented by the polynomial V = 4x^3 - 5x^2 + 2x. If the pool is filled to a height of 1 meter, what is the volume?

• 2 cubic meters

• 0.5 cubic meters

• 3 cubic meters

• 1 cubic meter

The height of a projectile can be modeled by the polynomial h(t) = -16t^2 + 32t + 48. What is the maximum height reached by the projectile?

• 48

• 80

• 64

• 32