Solving Equations by Factoring Worksheet

**Page 1**

1.

Find the value of $x$, which satisfies the equation |$x$^{2} + 7$x$| + 2$x$^{2} - 6 = 0 if $x$^{2} + 7$x$ > 0.

a. | - $\frac{3}{2}$ | ||

b. | 2 | ||

c. | $\frac{2}{3}$ | ||

d. | - 3 |

[Simplify.]

[Split into factors.]

[Equate each factor to zero.]

[Simplify.]

Therefore,

[As

Correct answer : (3)

2.

Andrew's garden is square shaped and Gary's garden is rectangular in shape. The length of the rectangular garden is longer by $a$ ft, and its width is $b$ ft shorter than the square garden. If both gardens have the same area, then find the dimensions of the rectangular garden. [$a$ = 9 ft and $b$ = 7 ft.]

a. | 72.0 ft × 40.5 ft | ||

b. | 40.5 ft × 24.5 ft | ||

c. | 40.5 ft × 38.5 ft | ||

d. | 24.5 ft × 56.0 ft |

If the dimensions of the square garden are

That is (

Square garden area =

Area of the rectangular garden = (

If the areas of 2 gardens are equal, then

So, the dimensions of the new rectangular garden are 40.5 ft × 24.5 ft.

[Substitute

Correct answer : (2)

3.

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)

4.

Solve ${(a-1.4)}^{2}$ = 0.

a. | - 2.8 | ||

b. | 2.8 | ||

c. | - 1.4 | ||

d. | 1.4 |

[Original equation.]

[Set repeated factor equal to 0.]

[Solve for

The solution of the equation

Correct answer : (4)

5.

Solve ($b$ - 9)($b$ - 13)^{2} = 0.

a. | - 9 and 13 | ||

b. | 9 and 13 | ||

c. | - 9 and - 13 | ||

d. | 9 and - 13 |

[Original equation.]

[Equate each factor to zero.]

[Solve for

The solutions of the equation (

Correct answer : (2)

6.

Solve (9$x$ - 20.7)(3$x$ + 10.8)^{2} = 0.

a. | 20.7 and - 10.8 | ||

b. | 22.7 and 3.6 | ||

c. | 2.3 and 13.8 | ||

d. | 2.3 and - 3.6 |

[Original equation.]

9

[Equate each factor to zero.]

[Solve for

The solutions of the equation (9

Correct answer : (4)

7.

Solve ($y$ - $\frac{1}{2}$)($y$ + 5) = 0.

a. | - $\frac{1}{2}$ and - 5 | ||

b. | - $\frac{1}{2}$ and 5 | ||

c. | $\frac{1}{2}$ and 5 | ||

d. | $\frac{1}{2}$ and - 5 |

[Original equation.]

(

[Equate each factor to zero.]

[Solve for

The solutions of the equation (

Correct answer : (4)

8.

Solve ($u$ - $\frac{3}{4}$)(5$u$ + 8)($\frac{1}{5}u$ - 7) = 0.

a. | $\frac{3}{4}$, $\frac{8}{5}$ and 7 | ||

b. | $\frac{3}{4}$, - $\frac{8}{5}$ and 35 | ||

c. | - $\frac{3}{4}$, $\frac{8}{5}$ and 7 | ||

d. | $\frac{3}{4}$, 3 and - 35 |

[Original equation.]

(

[Equate each factor to zero.]

[Solve for

The solutions of the equation (

Correct answer : (2)

9.

Solve the equation ($a$ - 4)($a$ + 4) = 0.

a. | - 4 and 0 | ||

b. | 4 and - 4 | ||

c. | 4 and 4 | ||

d. | - 4 and - 4 |

[Original equation.]

(

[Set each factor equal to zero.]

[Solve for

The solutions for the equation (

Correct answer : (2)

10.

Solve:

$f$($f$ + 2) = 0

a. | 0 and - 2 | ||

b. | 4 and - 4 | ||

c. | 0 and 2 | ||

d. | 2 and - 2 |

[Original equation.]

[Equate each factor to zero.]

[Simplify.]

The solutions of the equation

Correct answer : (1)