Math Is Fun Forum

ccmint

Member

Registered: 2009-10-11

Posts: 22

Need help with factoring.

I saw this problem on sosmath.com - http://www.sosmath.com/algebra/pfrac/pfrac.html

x^3 - 4x^2 + 5

and it's suppose to factor out to (x+1)(x^2-5x+5) and I've been sitting here trying to get it to that form but I only end up with (x^2+5)(x-4). Can someone please shed some light to how this can be factored out to (x+1)(x^2-5x+5). Thanks!

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Need help with factoring.

x = -1 can be spotted as a root of the equation quite easily as the coeffecients of the x^2 term and the 5 sum to 1.

(-1)^3 - 4(-1)^2 + 5 = -1 - 4 + 5 = 0

so you have:

(x+1)(x^2 + bx + c)  (coef. of x^2 is 1 since it's multiplied with x to give x^3)
x^3 + (b+1)x^2 + (c+b)x + c = x^3 - 4x^2 + 5

which gives immediately, b+1 = -4 -> b = -5,, c+b = 0 -> c = 5  (or just c = 5 immediately from other coef.)

(x+1)(x^2 - 5x + 5)

Last edited by luca-deltodesco (2009-10-25 20:32:46)

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ccmint

Member

Registered: 2009-10-11

Posts: 22

Re: Need help with factoring.

Thanks Luca for your response, but I'm still confused to how (x+1)(x^2-5x+5) was factored out from x^3-4x^2+5.

Is (x+1)(x^2+bx+x) a identity that has to be recognized through x^3-4x^2+5?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help with factoring.

Hi ccmint;

The fact that (x+1)(x^2-5x+5) are factors of x^3-4x^2+5 means that when multiplied:

[/math](x+1)(x^2-5x+5) = x^3-4x^2+5[/math]

When you know a root r, you can factor out an (x-r). Since Luca found  that x = -1 is a root, one factor is (x+1). Now just divide x^3-4x^2+5 by x+1 and you will get (x^2-5x+5).

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ccmint

Member

Registered: 2009-10-11

Posts: 22

Re: Need help with factoring.

Thanks Bobby and Luca. It all makes sense now.

Have a great day, John

Last edited by ccmint (2009-10-26 05:04:52)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help with factoring.

Hi ccmint;

Thanks, we are glad to help. Have a better day!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.