Solving Quadratic Equations by Factoring

Question 1

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?

Revolt · Accepted Answer

A:

Question 2

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?

Revolt · Accepted Answer

t: two possible amounts by which the dimensions were changed

Question 3

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

Revolt · Accepted Answer

x: x =  or x =

Question 4

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

Revolt · Accepted Answer

7: 7 or 12

Question 5

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

Revolt · Accepted Answer

x: x = 3 or x = 4

Question 6

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?

Revolt · Accepted Answer

2: 2 seconds

Question 7

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

Revolt · Accepted Answer

x: x = –6 or x = 1

Question 8

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?

Revolt · Accepted Answer

2: 240 tabletops

Question 9

The solutions to the equation are or

Question 10

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?

Revolt · Accepted Answer

4: 4 ft

Solving Quadratic Equations by Factoring Answers

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