Solving Quadratic Equations by Factoring Worksheet

**Page 1**

1.

Solve the equation ($a$ - 5)($a$ + 5) = 0.

a. | 5 and - 5 | ||

b. | 5 and 5 | ||

c. | -5 and + 5 | ||

d. | - 5 and 5 |

[Original equation.]

(

[Set each factor equal to zero.]

[Solve for

The solutions of the equation (

Correct answer : (1)

2.

What is the $x$-coordinate of the vertex of the graph of $y$ = 5(4$x$ + 9)($x$ + 3)?

a. | - $\frac{20}{7}$ | ||

b. | - $\frac{8}{21}$ | ||

c. | - $\frac{21}{8}$ | ||

d. | - $\frac{22}{9}$ |

[Original equation.]

0 = 5(4

[Substitute

(4

[Solve for

The

The

The

Correct answer : (3)

3.

The entrance door of a prison is in an inverse U-shape, similar to a parabola. If the shape of the door is modeled by a function $y$ = (-4/3^{2})(2$x$ + 4)(2$x$ - 4), then what is the width of the door at the base?

a. | 3 | ||

b. | 4 | ||

c. | 5 | ||

d. | 6 |

[Original equation.]

0 = (-4/3

[Substitute 0 for

(2

[Set each factor equal to zero.]

[Solve for

The width of the door at the base is 2 + 2 = 4 ft.

[Take positive value because the width cannot be negative.]

Correct answer : (2)

4.

Solve: ($e$ + 5)^{2} = 0

a. | -25 | ||

b. | 25 | ||

c. | -5 |

[Original equation.]

(

[Split into factors.]

(

[Equate each factor to zero.]

[Solve for

The solution of the equation (

Correct answer : (4)

5.

Solve: ($b$ - 7)^{2} = 0

a. | 7 | ||

b. | 12 | ||

c. | -12 | ||

d. | -7 |

[Original equation.]

(

[Split into factors.]

[Equate each factor to zero.]

[Simplify.]

The solution of the equation (

Correct answer : (1)

6.

Solve: (10$c$ - 9)^{2} = 0

a. | $\frac{9}{10}$ | ||

b. | $\frac{10}{9}$ | ||

c. | - $\frac{10}{9}$ | ||

d. | - $\frac{9}{10}$ |

[Original equation.]

(10

[Split into factors.]

(10

[Equate each factor to zero.]

10

[Simplify.]

[Divide each side by 10.]

The solution of the equation (10

Correct answer : (1)

7.

Solve: ($d$ - 5)(5$d$ - 11) = 0

a. | - 5 and - $\frac{11}{5}$ | ||

b. | 5 and - $\frac{11}{5}$ | ||

c. | 5 and $\frac{11}{5}$ | ||

d. | -5 and $\frac{11}{5}$ |

[Original equation.]

(

[Equate each factor to zero.]

[Simplify.]

The solutions of the equation (

Correct answer : (3)

8.

Solve: $f$($f$ + 3) = 0

a. | 3 and -3 | ||

b. | 0 and 3 | ||

c. | 5 and -5 | ||

d. | 0 and -3 |

[Original equation.]

[Equate each factor to zero.]

[Simplify.]

The solutions of the equation

Correct answer : (4)

9.

Solve: ($g$ - 3)($g$ + 3)($g$ - 4) = 0

a. | 3 and -3 or -4 | ||

b. | -3 and -3 or 4 | ||

c. | 3, -3 and 4 | ||

d. | 3 and 3 or -4 |

[Original equation.]

(

[Equate each factor to zero.]

[Simplify.]

The solutions of the equation (

Correct answer : (3)

10.

Solve: (4$h$ - 3)(5$h$ - 4)(6$h$ + 5) = 0

a. | -3/4, -4/5 and -5/6 | ||

b. | 3/4, 4/5 and -5/6 | ||

c. | -3/4, -4/5 and 5/6 | ||

d. | 3/4, 4/5 and 5/6 |

[Original equation.]

(4

[Equate each factor to zero.]

4

[Simplify.]

[Simplify to get the value of

The solutions of the equation (4

Correct answer : (2)