Grade 9 Quiz: Factoring Polynomials & Identifying Degrees

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 40 square meters, what are the dimensions of the garden? Identify the polynomial degree in your solution.

• Width: 3 meters, Length: 6 meters

• Width: 4 meters, Length: 7 meters

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

The height of a projectile is modeled by the equation h(t) = -4.9t^2 + 20t + 5, where h is the height in meters and t is the time in seconds. What is the maximum height reached by the projectile? Factor the polynomial to find the time when it hits the ground.

• Maximum height: 15.4 meters; Time when it hits the ground: approximately 6 seconds.

• Maximum height: 20 meters; Time when it hits the ground: approximately 5 seconds.

• Maximum height: 25.4 meters; Time when it hits the ground: approximately 4.12 seconds.

• Maximum height: 30 meters; Time when it hits the ground: approximately 3 seconds.

A car's distance from a starting point is given by the equation d(t) = 5t^2 + 10t, where d is in meters and t is in seconds. What is the degree of the polynomial, and how far does the car travel in 3 seconds?

• The degree of the polynomial is 2, and the car travels 75 meters in 3 seconds.

• The degree of the polynomial is 1, and the car travels 90 meters in 3 seconds.

• The degree of the polynomial is 3, and the car travels 60 meters in 3 seconds.

• The degree of the polynomial is 2, and the car travels 45 meters in 3 seconds.

The area of a triangular plot of land is given by the polynomial A(x) = 2x^2 + 8x. Factor this polynomial to find the dimensions of the base and height if the area is 24 square meters.

• Base: 4 meters, Height: 3 meters

• Base: 1 meter, Height: 24 meters

• Base: 8 meters, Height: 3 meters

• Base: 2 meters, Height: 6 meters

The profit P from selling x items is given by the polynomial P(x) = -2x^2 + 12x - 16. Factor this polynomial to find the number of items sold that results in zero profit.

• 2, 4

• 5

• 3

• 1

A rectangular swimming pool has a length that is twice its width. If the area of the pool is 200 square meters, write a polynomial equation to represent this situation and identify its degree.

• w^2 - 100 = 0, degree 2

• w^2 - 50 = 0, degree 1

• 2w^2 - 200 = 0, degree 2

• w^2 + 100 = 0, degree 1

The height of a box is modeled by the polynomial h(x) = x^2 - 4x + 4. Factor this polynomial to find the possible heights of the box when it is at maximum capacity.

• (x - 2)^2

• (x + 2)(x - 2)

• (x - 4)(x + 1)

• (x - 1)(x - 3)

A farmer has a field in the shape of a rectangle. The length is 5 meters more than twice the width. If the area of the field is 100 square meters, write a polynomial equation and identify its degree.

• w^2 + 5w - 100 = 0, degree 1

• 2w^2 + 10w - 100 = 0, degree 2

• 2w^2 + 5w - 100 = 0, degree 2

• 3w^2 + 5w - 100 = 0, degree 3

The revenue R from selling x units of a product is given by R(x) = 3x^2 + 12x. Factor this polynomial to determine the number of units sold when the revenue is zero.

• 5

• 0

• -3

• 10