Factoring Quadratic Expressions Worksheets Grade 10

1. Noah is building a rectangular sandbox for his younger sister. The area of the sandbox in square feet can be modeled by the quadratic expression 6x² + 19x + 10, where x is a positive integer representing the width in feet. If the length of the sandbox is (2x + 5) feet, what expression represents the width of the sandbox in terms of x?
2. A rectangular tile pattern is drawn on a coordinate plane. The tile's length is (x + 5) units and its width is (2x + 3) units. The area of the tile is expressed as a quadratic polynomial in standard form. What is the coefficient of the x term in this quadratic?
3. Factor completely: 6x² - 17x + 12 = ?

…and 5 more problems

1. Emma is designing a rectangular mural on a coordinate grid. The four corners of the mural are at (0,0), (3x+1,0), (3x+1,2x-3), and (0,2x-3). The area of the mural is 130 square units. Factor the quadratic expression that represents the area in terms of x to find the binomial factors. What are those binomial factors?
2. Factor completely: 6x² - 11x - 10 = ?
3. Kaia is designing a rectangular solar panel for a school project. The area of the panel is given by the polynomial 6x² + 23x - 18 square meters, where x is a positive integer representing a scaling factor. If the length of the panel is (3x - 2) meters, write an expression for the width of the panel in terms of x.

…and 5 more problems

1. Aroha is designing a rectangular kapa (traditional cloth) for a cultural exhibition. The area of the kapa in square meters is given by the quadratic expression 9x² + 39x + 42, where x is a positive integer representing a scaling factor. The length of the kapa is known to be (3x + 7) meters. What expression represents the width of the kapa in meters?
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (x,0), and (0,2x). The area of the triangle is 16 square units. Find the value of x.
3. Factor completely: 6x² - 13x - 5 = 0

…and 5 more problems