Polynomial Addition Worksheets Grade 9

1. (9x³ - 14x² + 22x - 8) + (12x³ + 8x² - 17x + 15) - (7x³ - 11x² + 9x - 4) = ?
2. A rectangular mosaic panel designed by Mere has its length represented by the polynomial (4x² + 6x - 8) centimeters and its width represented by (2x² - 4x + 10) centimeters. A square decorative tile is removed from the center of the panel. The side length of the square tile is represented by the polynomial (x² - 2x + 4) centimeters. What polynomial expression represents the remaining area of the mosaic panel after the square tile is removed?
3. A tech startup is designing a new smartphone with a rectangular screen. The screen's length is represented by the polynomial (4x² - 3x + 7) centimeters and its width is (2x² + 5x - 4) centimeters. The engineers need to calculate the total perimeter for the screen bezel. What simplified polynomial expression represents the perimeter of the smartphone screen in centimeters?

…and 4 more problems

1. A tech startup is modeling their quarterly profit using polynomial functions. Their revenue is modeled by R(x) = 4x³ - 2x² + 7x - 3, where x represents thousands of units sold. Their operating costs are modeled by C(x) = x³ + 5x² - 2x + 8. The company's board wants to understand their net profit function. What polynomial represents P(x), their quarterly profit?
2. Aroha is analyzing the budget for her small business. Her monthly revenue is modeled by the polynomial \( R(x) = 9x^2 + 14x - 11 \) dollars, and her monthly expenses are modeled by \( E(x) = 4x^2 - 7x + 13 \) dollars, where \( x \) represents the number of units sold in hundreds. Aroha needs to determine her monthly profit, which is revenue minus expenses. What simplified polynomial expression represents her monthly profit, \( P(x) \)?
3. (3x² - 2x + 5) + (2x² + 4x - 3) - (x² - 3x + 1) = ?

…and 4 more problems

1. Mason is designing a geometric mosaic on a coordinate grid. The perimeter of the mosaic is defined by four vertices: A (0, 0), B (2x² + 7, 0), C (2x² + 7, 2x - 7), and D (0, 2x - 7). A smaller triangular section is removed from one corner, with vertices at (0, 0), (x² + 2, 0), and (0, x - 2). What polynomial expression represents the remaining area of the mosaic after the triangular section is removed?
2. A tech startup is modeling their quarterly revenue using polynomial functions. Their revenue from software sales is represented by R_s(x) = 4x³ - 2x² + 5x - 3, while their hardware revenue is R_h(x) = -2x³ + 7x² - 4x + 8, where x represents the quarter number. What polynomial expression represents their total quarterly revenue?
3. A technology company is designing a new smartphone with a rectangular screen. The screen's length is represented by the polynomial (4x² - 3x + 7) millimeters and its width is (2x² + 5x - 4) millimeters. The engineers need to calculate the total length of the protective bezel that will frame the screen. What polynomial expression represents the perimeter of the smartphone screen in millimeters?

…and 3 more problems