Factor Polynomials Worksheets Grade 9

1. Hana is designing a rectangular metal sheet for a sculpture. The area of the sheet is given by the polynomial 28x⁴ + 20x³ - 12x² square centimeters. She needs to factor out the greatest common factor (GCF) to simplify her design calculations. What is the factored form of this polynomial?
2. Hana is designing a rectangular garden for a community project. The area of the garden is represented by the polynomial 16x² + 24x square meters, where x is a positive integer representing the width in meters. She needs to factor this polynomial to find the length and width expressions. What is the factored form of the polynomial 16x² + 24x?
3. Liam is designing a rectangular garden for his community center. The area of the garden can be modeled by the polynomial expression 6x² + 11x - 10, where x represents the length in meters. To determine the optimal layout, Liam needs to factor this expression completely to find its binomial dimensions. What is the factored form of the area?

…and 4 more problems

1. Charlotte is designing a rectangular mosaic where the area is represented by the polynomial 16x³ + 40x² + 24x square inches. The mosaic is composed of square tiles. If the height of the mosaic is (2x + 3) inches, what is the width of the mosaic in factored form?
2. Factor completely: 12x³ - 27x² - 15x = ?
3. A rectangular garden has an area represented by the polynomial expression 12x²y + 18xy² - 24xy. If the width of the garden is 6xy, what is the length of the garden in simplest form?

…and 5 more problems

1. A manufacturing company is designing a new storage container with a volume represented by the polynomial 4x³ - 8x² - 12x cubic feet. The engineers need to factor out the greatest common factor to determine the base dimensions. What is the greatest common factor of the polynomial 4x³ - 8x² - 12x?
2. A manufacturing company is designing a new storage container with a volume represented by the polynomial 12x³ - 3x² - 27x cubic centimeters. The engineers need to factor out the greatest common factor to determine the base dimensions for standard packaging. What is the greatest common factor of this polynomial?
3. Mere is designing a rectangular metal frame. The area of the frame is given by the polynomial 28x³ + 21x² − 14x square centimeters. If the width of the frame is 7x centimeters, write a fully factored expression for the length of the frame.

…and 6 more problems