Polynomial Addition Worksheets Grade 9

1. (3x² - 5x + 7) + (2x² + 4x - 9) - (x² - 3x + 2) = ?
2. (3x² - 2x + 5) + (2x² + 4x - 3) = ?
3. Aroha is designing a geometric pattern on a coordinate grid. The pattern consists of a quadrilateral with vertices at (x² + 3x - 1, 0), (0, 5x² - x + 3), (-x² + 2x + 7, 0), and (0, -3x² + 4x - 5). The perimeter of the quadrilateral is found by adding the lengths of its four sides, each represented by a polynomial expression. One side connects (x² + 3x - 1, 0) to (0, 5x² - x + 3) and is represented by the polynomial (5x² + 4x + 4). The second side connects (0, 5x² - x + 3) to (-x² + 2x + 7, 0) and is represented by (7x² - 3x + 10). The third side connects (-x² + 2x + 7, 0) to (0, -3x² + 4x - 5) and is represented by (5x² - 2x + 5). The fourth side connects (0, -3x² + 4x - 5) to (x² + 3x - 1, 0) and is represented by (3x² + x + 3). What is the simplified polynomial expression for the total perimeter of the quadrilateral?

…and 3 more problems

1. Isabella is designing a rectangular mural for her school's art competition. The length of the mural is represented by the polynomial (5x² - 8x + 12) feet, and the width is represented by (3x² + 7x - 9) feet. The school's art director decides to add a decorative trim along the entire perimeter of the mural. What simplified polynomial expression represents the total length of trim needed in feet?
2. A tech startup is designing a new smartphone case. The case's length is represented by the polynomial (4x² - 3x + 7) cm and its width is (2x² + 5x - 2) cm. The company wants to add a protective rubber bumper that runs along the entire perimeter. What simplified polynomial expression represents the total length of bumper needed?
3. (2x³ - 5x² + 3x - 7) + (4x³ + 2x² - 8x + 5) - (3x³ - x² + 6x - 2) = ?

…and 5 more problems

1. A triangular garden plot is drawn on a coordinate grid. The vertices are at A (2x - 3, 0), B (0, 4x + 7), and C (x^2 + 2x, x^2 - 3x + 2). A walkway runs along the perimeter of the triangle. The length of side AB is (5x^2 - 7x + 2) units, side BC is (3x^2 + 4x - 7) units, and side CA is (2x^2 + 7x + 2) units. What is the total length of the walkway around the triangular garden plot, expressed as a simplified polynomial?
2. Aroha is a landscape architect designing a park that features two adjacent rectangular flower beds. The length of the first flower bed is represented by the polynomial (9x² - 11x + 13) meters, and its width is (7x² + 10x - 8) meters. The second flower bed has a length of (6x² + 14x - 9) meters and a width of (5x² - 12x + 15) meters. The city council wants to install an LED light strip around the combined perimeter of both flower beds. What simplified polynomial expression represents the total length of light strip needed, in meters?
3. 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?

…and 3 more problems