Solving Quadratic Equations by Factoring Answers

A rectangular patio is 9 ft by 6 ft. When the length and width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6 + x)(9 + x) = 88. What does the value of x in her solutions represent?

What are the solutions to the equation (x – 6)(x + 8) = 0?

Use the zero product property to find the solutions to the equation x2 + 12 = 7x.

What are the solutions to the equation (2x – 5)(3x – 1) = 0?

A rectangular field has an area of 1,764 m2. The width of the field is 13 m more than the length. What is the perimeter of the field?

The hypotenuse of a right triangle is 52 in. One leg of the triangle is 8 in. more than twice the length of the other. What is the perimeter of the triangle?

A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. ft. By how much were the dimensions increased?

Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12.

What are the solutions to the equation 3(x – 4)(x + 5) = 0?

The solutions to a quadratic equation are x = 2 and x = 7. If k is a nonzero constant, which of the following must be equal to the quadratic equation?