Factor Trinomials Worksheets Grade 9

1. A rectangular garden has an area of (6x² + 19x + 10) square meters. If the length of the garden is (3x + 2) meters, what is the width of the garden in terms of x?
2. Aroha is constructing a rectangular wooden frame for a school art installation. The area of the frame's surface (in square meters) is given by the quadratic expression 9x² + 39x + 42, where x is a positive integer representing the width in meters. The length and width of the frame are both binomial expressions with integer coefficients. Using the AC method, factor this quadratic expression to find the binomial expressions that represent the possible dimensions of the frame.
3. A physics class is designing a catapult that launches projectiles. The height of a projectile above ground is modeled by the quadratic equation h(t) = -16t² + 64t + 80, where h is height in feet and t is time in seconds. Factor this quadratic expression completely to find the time when the projectile hits the ground.

…and 4 more problems

1. A physics class is designing a projectile motion experiment where the height of a ball above ground is modeled by the quadratic equation h(t) = 3t² + 11t + 6, where h is height in meters and t is time in seconds. The teacher asks students to factor this expression to determine at what times the ball will be at ground level. Using the AC method, what is the factored form of this quadratic expression?
2. A rectangular garden has an area represented by the quadratic expression 2x² + 7x + 6 square meters, where x represents the width in meters. The length of the garden is 5 meters more than its width. Factor the quadratic expression to determine the binomial expressions that represent the garden's dimensions.
3. Charlotte is designing a rectangular garden for a school project. The area of the garden (in square meters) is represented by the quadratic expression 8x² + 26x + 15, where x is a positive integer representing the width in meters. The length and width of the garden are both binomial expressions with integer coefficients. Using the AC method, factor this quadratic expression to find the binomial expressions that represent the garden's dimensions.

…and 3 more problems

1. Aroha is designing a rectangular mosaic on a coordinate grid. The area of the mosaic, in square units, is given by the quadratic expression 14x² + 41x + 15. She partitions the rectangle into four smaller rectangles using the area model method, where the length and width of the whole rectangle are binomial expressions with integer coefficients. What is the factored form representing the dimensions of Aroha's mosaic?
2. Factor: 15x² + 34x + 15
3. Olivia is designing a rectangular flower bed for a community garden project. The area of the flower bed is given by the quadratic expression 9x² + 21x + 10 square feet, where x represents the width in feet. The length and width of the flower bed are both binomial expressions with integer coefficients. Using the AC method, factor this quadratic expression to find the possible dimensions of the flower bed.

…and 4 more problems