Stuck on polynomial

hubbylax · Mar 26, 2006

I solved all the other problems for homework except these:
Factor the following:

1) x^3+8
Tried (x+2) (x-2) (x-2) but that didn't work

and
2) 8x^3-125
Tried (2x-5) (2x+5) (2x-5) but that didn't work either!

Any ideas? Thanks for your help!

stapel · Mar 26, 2006

Hint 1: Sum-of-cubes formula.

Hint 2: Difference-of-cubes formula.

Eliz.

hubbylax · Mar 26, 2006

Great! thanks!

So that makes the answers:
1) (x+2) (x^2-2x+4)

and
2) (2x-5) (4x^2+10x+25)

I was trying to break it into three binomials.

Thanks again!

Mrspi · Mar 26, 2006

hubbylax said:
I solved all the other problems for homework except these:
Factor the following:

1) x^3+8
Tried (x+2) (x-2) (x-2) but that didn't work

and
2) 8x^3-125
Tried (2x-5) (2x+5) (2x-5) but that didn't work either!

Any ideas? Thanks for your help!

Here are two factoring patterns that you either need to memorize, or tattoo on your arm (and memorizing is cheaper and lots less painful!):

a3 + b3 = (a + b)(a2 - ab + b2)

a3 - b3 = (a - b)(a2 + ab + b2)

Your first problem is
x3 + 8

Do you recognize that 8 is 23?
So, you have
x3 + (2)3
Use the first pattern to factor.

Your second problem is
8x3 - 125

You can write 8x3 as (2x)3
You can write 125 as (5)3

So, you have
(2x)3 - (5)3
Use the second pattern.

Stuck on polynomial

hubbylax

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stapel

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hubbylax

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Mrspi

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