Factor Polynomials Worksheets Grade 9

1. Noah is designing a geometric pattern on a coordinate grid. The pattern consists of a series of rectangles. The first rectangle has a width represented by the monomial 6x and a length represented by the binomial (x + 1). The area of this rectangle is 6x² + 6x square units. The second rectangle has a width of 6x and a length of (2x + 3), giving it an area of 12x² + 18x square units. If Noah combines these two rectangles into a single larger rectangle by placing them side by side along their widths, what is the total combined area of the larger rectangle, factored completely by its greatest common factor?
2. Liam is designing a rectangular garden with an area represented by the polynomial expression 3x² + 15x + 18 square feet. He needs to determine the greatest common factor of this expression to help him plan equal planting sections. What is the greatest common factor of the polynomial 3x² + 15x + 18?
3. Factor completely: 15x³ - 35x² - 30x = ?

…and 4 more problems

1. A rectangular prism has a volume represented by the polynomial 24x³y² - 36x²y³ + 48x⁴y. If the height of the prism is 12xy, what is the area of the base in simplest form?
2. Liam is designing a rectangular garden with an area represented by the polynomial expression 2x² + 7x + 6 square meters. He needs to determine the dimensions of the garden in terms of binomial factors. What are the length and width of Liam's garden when expressed as factors of this polynomial?
3. A manufacturing company is designing a new packaging box with a volume represented by the polynomial 4x³ + 18x² + 20x cubic centimeters. The height of the box is 2x cm, and the length is (x + 2) cm. What expression represents the width of the box in terms of x?

…and 5 more problems

1. Factor completely: 27x⁴y² - 72x³y³ + 36x²y⁴ = ?
2. Factor completely: 42x⁴y³ - 63x³y⁴ + 21x²y⁵ = ?
3. A rectangular community garden plot has an area represented by the polynomial 12x² - 7x - 10 square meters. The garden committee needs to install decorative fencing along the perimeter and must determine the dimensions in factored form. If the length is represented by (4x - 5) meters, what expression represents the width of the garden plot?

…and 5 more problems