Factoring and the Distributive Property Question

Hi all,

I've been struggling a little with my algebra so during the summer break I've been working through the book Algebra Demystified and it's really helping.

But I've come across a question half way through that I can't solve, I'm not sure how to tackle it, the question and answer are

$\displaystyle x^{3}+5x^{2}-x-5=(x-1)(x+1)(x+5)$

Any tips or a starting point would be greatly appreciated.

Thanks.

Re: Factoring and the Distributive Property Question

Quote:

Originally Posted by

**Srengam** the question and answer are

$\displaystyle x^{3}+5x^{2}-x-5=(x-1)(x+1)(x+5)$

This is not a question; this is an equality.

Re: Factoring and the Distributive Property Question

Hi, Srengam. First, kudos for working through this stuff!

Typically cubics (when the highest power of x is 3) are not easy to factor. However, the one you have can be done if you group the first two terms together $\displaystyle x^{3}$ and $\displaystyle 5x^{2}$, and group the second two terms $\displaystyle -x$ and -5 together, then factoring these groupings individually.

If that's not clear, let me know and I will write up what I mean more explicitly. Good luck!

Re: Factoring and the Distributive Property Question

Quote:

Originally Posted by

**Srengam** But I've come across a question half way through that I can't solve, I'm not sure how to tackle it, the question and answer are

$\displaystyle x^{3}+5x^{2}-x-5=(x-1)(x+1)(x+5)$

Note that $\displaystyle x^{3}+5x^{2}-x-5=x^2(x+5)-(x+5)=(x^2-1)(x+5)$

Re: Factoring and the Distributive Property Question

Thanks all,

I can see now what I need to "pull out" to simplify it all.

Thanks again.