Factoring Quadratic Expressions Worksheets Grade 10

1. 3x² - 10x - 8 = 0
2. A physics class is designing a parabolic water fountain where the water's path follows the equation h(t) = -5t² + 20t + 1, where h is the height in meters and t is time in seconds. The students want to know at what times the water will reach a height of 16 meters. Solve the equation -5t² + 20t + 1 = 16 to find these times.
3. Factor: 8x² + 26x + 15

…and 5 more problems

1. A rectangular garden has a length that is 3 meters more than twice its width. The area of the garden is 65 square meters. If you were to draw this garden on a coordinate plane with one corner at the origin and sides along the axes, what would be the dimensions of the rectangle?
2. Noah is building a rectangular sandbox for his younger sister. The area of the sandbox in square feet can be modeled by the quadratic expression 6x² + 19x + 10, where x is a positive integer representing the width in feet. If the length of the sandbox is (2x + 5) feet, what expression represents the width of the sandbox in terms of x?
3. A rectangular garden has an area that can be modeled by the quadratic expression 2x² + 7x + 6 square meters, where x represents the width in meters. If the length is 5 meters longer than the width, determine the actual dimensions of the garden.

…and 5 more problems

1. Emma is designing a rectangular flower bed in her backyard. The area of the flower bed can be modeled by the quadratic expression 3x² + 23x + 14 square feet, where x is a positive integer representing the width in feet. If the length of the flower bed is (3x + 2) feet, what expression represents the width of the flower bed in terms of x?
2. A right triangle is positioned on a coordinate plane with vertices at (0,0), (2x,0), and (0,x-3). The area of this triangle is 20 square units. Find the positive value of x that satisfies this condition.
3. Factor: 12x² - 17x - 7 = ?

…and 5 more problems