# Factorising explaination

• Oct 2nd 2007, 08:07 PM
Local_lunatic
Factorising explaination
I've just been doing some revising and I came across a couple of factorisation questions that im not quite sure how to work out.

$\displaystyle x^4 - a6$

and

$\displaystyle x - x^5$

So if anyone could explain how to do them it would be really useful.
• Oct 2nd 2007, 08:17 PM
earboth
Quote:

Originally Posted by Local_lunatic
I've just been doing some revising and I came across a couple of factorisation questions that im not quite sure how to work out.

$\displaystyle x^4 - a6$

and

$\displaystyle x - x^5$

So if anyone could explain how to do them it would be really useful.

hello,

I assume that you mean: $\displaystyle x^4-a^6$ . This is a difference of squares which can be factored to:

$\displaystyle x^4-a^6 = (x^2 - a^3)(x^2 + a^3)$

$\displaystyle x-x^5 = x(1-x^4)$ . Factor out (?) the common factor. You get the result in the bracket by dividing each summand by the factor in front of the bracket:

$\displaystyle x-x^5 = x\left(\frac xx-\frac{x^4}{x}\right) = x(1-x^4)$
• Oct 2nd 2007, 09:46 PM
Local_lunatic
Quote:

Originally Posted by earboth
hello,

I assume that you mean: $\displaystyle x^4-a^6$ . This is a difference of squares which can be factored to:

$\displaystyle x^4-a^6 = (x^2 - a^3)(x^2 + a^3)$

$\displaystyle x-x^5 = x(1-x^4)$ . Factor out (?) the common factor. You get the result in the bracket by dividing each summand by the factor in front of the bracket:

$\displaystyle x-x^5 = x\left(\frac xx-\frac{x^4}{x}\right) = x(1-x^4)$

That's the answer I got for the second one too, but the book had a different one. Actually, the answer comes to the same thing it's just written differently.

$\displaystyle x(1+x^2)(1+x)(1+x)$

Which one am I meant to do in a test?
• Oct 3rd 2007, 05:24 PM
SnipedYou
Are you sure it doesn't say $\displaystyle x(1+x^{2})(1+x)(1-x)$? You wouldn't wanna make a typo like that on a test (I have done it before and lost 5 points for one sign so watch for it)
• Oct 3rd 2007, 08:23 PM
CaptainBlack
Quote:

Originally Posted by Local_lunatic
That's the answer I got for the second one too, but the book had a different one. Actually, the answer comes to the same thing it's just written differently.

$\displaystyle x(1+x^2)(1+x)(1+x)$

Which one am I meant to do in a test?

If the question asks you to factorise something full marks will be given
for as complete a factorisation as possible under the constraints you
are expected to observe (probably factors with real coefficients).

RonL