1. ## 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.

$x^4 - a6$

and

$x - x^5$

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

2. 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.

$x^4 - a6$

and

$x - x^5$

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

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

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

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

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

3. Originally Posted by earboth
hello,

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

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

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

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

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

Which one am I meant to do in a test?

4. Are you sure it doesn't say $x(1+x^{2})(1+x)(1-x)$? 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)

5. 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.

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

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