Polynomial Division Worksheets Grade 9

1. (45x⁸y⁷ - 60x⁶y⁹ + 75x⁷y⁵) ÷ (15x⁴y³) = ?
2. A triangular garden is designed with vertices at coordinates A(0,0), B(4x,0), and C(0,3x). The gardener wants to divide the triangle into smaller congruent triangles by drawing lines parallel to the sides, creating a grid pattern. If the area of the original triangle is represented by the polynomial (6x²) square units and each small triangle has area (x²/2) square units, how many small congruent triangles are created in total?
3. (24x⁷y⁵ - 36x⁵y⁷ + 48x⁶y⁴) ÷ (12x³y²) = ?

…and 5 more problems

1. A robotics team is designing a solar-powered drone with wing panels that generate electricity. The total power output from all panels is represented by the polynomial 15x⁴y³ - 25x³y⁴ + 35x²y⁵ watts. If this power needs to be distributed equally among 5x²y² identical battery systems, what simplified polynomial expression represents the power allocated to each battery system?
2. A triangular garden plot has vertices at coordinates A(0,0), B(4x,0), and C(2x,3x²). The gardener wants to divide the triangle into two equal areas by drawing a horizontal line parallel to the base AB. At what y-coordinate should this dividing line be placed?
3. A robotics team is designing a solar panel with a rectangular area represented by the polynomial 12x³y² + 18x²y³ - 6xy⁴ square centimeters. If they want to divide this panel into strips of equal width, where each strip has an area of 3xy² square centimeters, how many strips can they create? Express your answer as a simplified polynomial.

…and 4 more problems

1. Kaia is a materials engineer designing a composite beam for a bridge. The total cross-sectional area of the beam is represented by the polynomial 27x⁵y³ - 45x⁴y⁴ + 18x³y⁵ square centimeters. The beam is composed of several identical rectangular layers stacked vertically, each with a thickness of 9x²y³ centimeters. What simplified polynomial expression represents the total width of all layers combined?
2. A robotics team is designing a solar panel array with a total area represented by the polynomial 15x⁴y³ - 25x³y⁴ + 35x²y⁵ square meters. They need to divide this area equally among 5x²y² identical solar panels. What simplified polynomial expression represents the area of each individual solar panel?
3. Sophia is analyzing a rectangular prism with a square base. The side length of the square base is (3x) units, and the height of the prism is (2x² + 5x - 7) units. She wants to find the volume of the prism and then divide that volume by the area of the square base to find the height. However, she makes a mistake: she accidentally divides the volume by the side length of the base (3x) instead of the area. What simplified polynomial expression does she incorrectly get for the height?

…and 4 more problems