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Homework: Factoring Expressions

Module by: Kenny M. Felder. E-mail the author

Summary: Homework set on factoring quadratics.

Factor the following expressions.

Exercise 1

3x 3 + 15 x 2 + 18 x 3x 3 + 15 x 2 + 18 x size 12{3x rSup { size 8{3} } +"15"x rSup { size 8{2} } +"18"x} {}

Check your answer by multiplying back.

Exercise 2

x 2 − 12 x + 32 x 2 − 12 x + 32 size 12{x rSup { size 8{2} } - "12"x+"32"} {}

Check your answer by plugging the number 4 into both my original expression, and your factored expression. Did they come out the same?

Is there any number xx size 12{x} {} for which they would not come out the same?

Exercise 3

x 2 − 4x − 32 x 2 − 4x − 32 size 12{x rSup { size 8{2} } - 4x - "32"} {}

Exercise 4

x8 2 − 18 y 4 x8 2 − 18 y 4 size 12{x8 rSup { size 8{2} } - "18"y rSup { size 8{4} } } {}

Exercise 5

x 2 + 18 x + 32 x 2 + 18 x + 32 size 12{x rSup { size 8{2} } +"18"x+"32"} {}

Exercise 6

x 2 − 18 x + 32 x 2 − 18 x + 32 size 12{x rSup { size 8{2} } - "18"x+"32"} {}

Exercise 7

2x 2 + 12 x + 10 2x 2 + 12 x + 10 size 12{2x rSup { size 8{2} } +"12"x+"10"} {}

Exercise 8

100 x 2 + 8000 x + 1000 100 x 2 + 8000 x + 1000 size 12{"100"x rSup { size 8{2} } +"8000"x+"1000"} {}

Exercise 9

x 2 + 4x − 32 x 2 + 4x − 32 size 12{x rSup { size 8{2} } +4x - "32"} {}

Exercise 10

x 4 − y 4 x 4 − y 4 size 12{x rSup { size 8{4} } - y rSup { size 8{4} } } {}

Exercise 11

x 2 + 13 x + 42 x 2 + 13 x + 42 size 12{x rSup { size 8{2} } +"13"x+"42"} {}

Exercise 12

x 2 + 16 x 2 + 16 size 12{x rSup { size 8{2} } +"16"} {}

Exercise 13

4x 2 − 9 4x 2 − 9 size 12{4x rSup { size 8{2} } - 9} {}

Exercise 14

3x 2 − 48 3x 2 − 48 size 12{3x rSup { size 8{2} } - "48"} {}

Exercise 15

2x 2 + 10 x + 12 2x 2 + 10 x + 12 size 12{2x rSup { size 8{2} } +"10"x+"12"} {}

Exercise 16

x 2 − 9 x 2 − 9 size 12{x rSup { size 8{2} } - 9} {}

Exercise 17

2x 2 + 11 x + 12 2x 2 + 11 x + 12 size 12{2x rSup { size 8{2} } +"11"x+"12"} {}

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