Factor Quadratics Worksheets Grade 9

1. 2x² - 11x + 12 = ?
2. A local theater is designing a new stage backdrop that will have a rectangular opening for special effects. The area of the opening is given by the quadratic expression 3x² + 10x + 8 square feet, where x represents the additional length beyond the minimum dimensions. The theater director knows that the width of the opening is (x + 2) feet. What expression represents the length of the opening in factored form?
3. A rectangular garden has an area that can be expressed as 2x² + 7x + 6 square meters. If the length of the garden is (2x + 3) meters, what is the width of the garden in terms of x?

…and 4 more problems

1. A construction company is designing a rectangular parking lot with an area represented by the polynomial 3x² + 10x - 8 square meters. The length of the parking lot is given as (x + 4) meters. What expression in factored form represents the width of the parking lot?
2. 2x² + 7x + 3 = ?
3. Factor completely: 12x² + 37x + 21 = ?

…and 5 more problems

1. Factor completely: 8x² + 34x + 21 = ?
2. A physics student is analyzing the trajectory of a rocket launched from ground level. The height of the rocket above the ground is modeled by the quadratic function h(t) = -5t² + 40t, where h is the height in meters and t is the time in seconds after launch. Factor this quadratic expression to determine at what time the rocket will return to the ground.
3. A physics class is designing a model rocket launch. The height of the rocket above ground is modeled by the function h(t) = -16t² + 96t + 112, where t is time in seconds. Factor this quadratic expression completely to determine at what time the rocket will hit the ground.

…and 5 more problems