Factoring Trinomials Worksheet

**Page 1**

1.

Solve 2$x$^{2} + 3$x$ - 18 = $x$^{2} by factorizing.

a. | $x$ = -6 or $x$ = -3 | ||

b. | $x$ = 6 or $x$ = 3 | ||

c. | $x$ = -6 or $x$ = 3 | ||

d. | None of the above |

[Original equation.]

[Write the equation in the standard form.]

(

[Factorize the equation.]

[Apply zero product property.]

The values of

Correct answer : (3)

2.

Factor: $x$^{2} + 12$x$ + 35

a. | ($x$ - 7)($x$ - 5) | ||

b. | ($x$ + 7)($x$ + 5) | ||

c. | ($x$ - 8)($x$ + 5) | ||

d. | ($x$ + 7)($x$ - 5) |

Compare the equation with

Find the numbers

1,35 36

7, 5 12

The required values of

So, the factors of the equation

Correct answer : (2)

3.

Factor: $x$^{2} - 3$x$ + 2

a. | ($x$ - 1)($x$ + 2) | ||

b. | ($x$ - 1)($x$ - 2) | ||

c. | ($x$ + 1)($x$ - 2) | ||

d. | ($x$ + 1)($x$ + 2) |

Compare the equation with

Since

-1, -2 - 3

The required values of

So, the factors of the equation

Correct answer : (2)

4.

Factor: $x$^{2} + 3$x$ - 10

a. | ($x$ - 2)($x$ - 5) | ||

b. | ($x$ + 2)($x$ - 5) | ||

c. | ($x$ + 2)($x$ + 5) | ||

d. | ($x$ - 2)($x$ + 5) |

Compare the equation with

Since

-1, 10 9

-2, 5 3

The required values of

The factors of the equation

Correct answer : (4)

5.

Factor: $x$^{2} - 3$x$ - 18

a. | ($x$ - 6)($x$ + 3) | ||

b. | ($x$ - 6)($x$ - 3) | ||

c. | ($x$ + 6)($x$ - 3) | ||

d. | ($x$ + 6)($x$ + 3) |

Compare the equation with

Since

-3, 6 3

-6, 3 -3

The required values of

The factors of equation

Correct answer : (1)

6.

Factor: $x$^{2} - 4$x$ - 21

a. | ($x$ + 7)($x$ - 3) | ||

b. | ($x$ + 7)($x$ + 3) | ||

c. | ($x$ - 7)($x$ + 3) | ||

d. | ($x$ - 7)($x$ - 3) |

Compare the equation with

Since

-3, 7 4

-7, 3 -4

The required values of

So, the factors of equation

Correct answer : (3)

7.

Factor: $x$^{2} + 4$x$ - 12

a. | ($x$ - 2)($x$ - 6) | ||

b. | ($x$ + 2)($x$ + 6) | ||

c. | ($x$ + 2)($x$ - 6) | ||

d. | ($x$ - 2)($x$ + 6) |

Compare the equation with

Since

-6, 2 -4

-2, 6 4

The required values of

So, the factors of the equation

Correct answer : (4)

8.

Factor: $x$^{2} - 7$x$ + 10

a. | ($x$ + 5)($x$ - 2) | ||

b. | ($x$ + 5)($x$ + 2) | ||

c. | ($x$ - 5)($x$ - 2) | ||

d. | ($x$ - 5)($x$ + 2) |

Compare the equation with

Since

-5, -2 -7

The required values of

So, the factors of the equation

Correct answer : (3)

9.

Solve: $x$^{2} + 17$x$ + 70 = 0

a. | $x$ = -7 or $x$ = -10 | ||

b. | $x$ = 7 or $x$ = 10 | ||

c. | $x$ = 7 or $x$ = -10 | ||

d. | $x$ = -7 or $x$ = 10 |

[Original equation.]

The factors are 7 and 10.

[7 + 10 = 17 and 7 x 10 = 70]

(

[Factorize the equation.]

[Apply zero product property.]

The values of

Correct answer : (1)

10.

Solve: $x$^{2} - 19$x$ + 88 = 0

a. | $x$ = 8 or $x$ = 11 | ||

b. | $x$ = -8 or $x$ = -11 | ||

c. | $x$ = -8 or $x$ = 11 | ||

d. | $x$ = 8 or $x$ = -11 |

[Original equation.]

The factors are -8 and -11.

[-8 + (-11) = -19 and (-8) x (-11) = 88]

(

[Factorize the equation.]

[Apply zero product property.]

The values of

Correct answer : (1)