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#1 2007-09-17 17:19:01

wowjustwow
Member
Registered: 2007-09-17
Posts: 0

Show me the steps to factoring this polynomial: x^4 - 4x^3 + 6x^2 - 4x

Thanks!

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#2 2007-09-17 18:01:33

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Show me the steps to factoring this polynomial: x^4 - 4x^3 + 6x^2 - 4x

Firstly we can factor out the x:

Now recall the factor theorem:
If for a polynomial, P(x), P(a) = 0 then x-a is a factor.

Note: You don't need the factored out x in any of the following steps, although you do need to put it back in the end. Can you figure out why?

Now we can test values of x to find more factors .
Let's try x=1:

   Nope
How about 2:
   Yes! x-2 is a factor!

Now, using long division, divide

by
.

You should hopefully get

So the fully factored expression is

Last edited by Identity (2007-09-17 18:01:59)

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#3 2007-09-17 21:21:55

wowjustwow
Member
Registered: 2007-09-17
Posts: 0

Re: Show me the steps to factoring this polynomial: x^4 - 4x^3 + 6x^2 - 4x

Splendid!

Thanks for pointing me in the right direction.

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