Perfect Square Trinomials Worksheets Grade 9

1. Factor: 25x² - 60x + 36 = ?
2. 49x² + 112x + 64 = ?
3. An engineer is designing a square solar panel array for a new satellite. The total area of the array can be modeled by the expression 9x² + 42x + 49 square centimeters, where x represents the additional length needed for mounting hardware. Recognizing this as a perfect square trinomial, the engineer needs to factor it to determine the side length of the square array. What is the factored form of this expression?

…and 4 more problems

1. Liam is designing a rectangular garden with an area that can be expressed as the trinomial x² + 14x + 49 square feet. He realizes this area represents a perfect square. What is the factored form of this expression, which would give the side length of the square garden?
2. A company's quarterly profit in thousands of dollars is modeled by the quadratic function P(x) = 4x² + 28x + 49, where x represents the quarter number. The company's financial analyst notices this can be factored as a perfect square trinomial. What is the value that completes the square: (2x + k)²?
3. Ava is a structural engineer designing a square-shaped steel support platform for a bridge. The area of the platform (in square meters) is given by the perfect square trinomial 144x² + 120x + 25, where x represents a scaling factor for the platform's dimensions. Ava needs to factor this expression to find the binomial that represents the side length of the square platform. What is the factored form of 144x² + 120x + 25?

…and 4 more problems

1. Charlotte is designing a square-shaped community garden. The city planning department requires that the total area of the garden (in square meters) be expressed as the trinomial 81x² + 144x + 64, where x represents the number of additional meters added to the original side length. Charlotte recognizes this as a perfect square trinomial and needs to factor it to determine the side length of the square garden. What is the factored form of this expression?
2. Kaia is a structural engineer designing a square-shaped support platform for a large sculpture. The area of the platform (in square meters) is given by the perfect square trinomial 144x² - 264x + 121, where x represents a scaling factor for the dimensions. Kaia needs to factor this expression to find the binomial that represents the side length of the square platform. What is the factored form of 144x² - 264x + 121?
3. A square-shaped mosaic floor in a museum lobby has an area represented by the expression 9x² + 42x + 49 square feet. The mosaic is made up of smaller square tiles arranged in a grid pattern. If the side length of the entire mosaic can be written as (ax + b) feet, where a and b are positive odd integers, what is the binomial expression for the side length?

…and 4 more problems