Solving Quadratic Equations by Factoring Answers

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?

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 (2x – 5)(3x – 1) = 0?

The square of 9 less than a number is 3 less than the number. What is the number?

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

The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32t – 16t2. How long after launch does the projectile return to the ground?

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

The profit a company makes from producing x tabletops is modeled by the equation P(x) = 480x – 2x2. For what number of tabletops does the company make a profit of $0?

The solutions to the equation are or

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?