Factorising certain polynomials During lesson we were given a starter activity which was to try and factorise polynomials and see what happened.
The polynomials were
$x^3-8$,
$x^3-3x^2+ x -3$
and
$x^4 - 16$.
I could not work out what happened to them, and it's bugging me. If anyone can explain then it'd be helpful! Thank you.

a^3 - b^3 = (a - b)(a^2 + ab + b^2). So x^3 - 8 = (x - 2)(x^2 + 2x + 4).
For x^3 - 3x^2 + x - 3, factor by grouping the first two terms together and taking out the GCF and grouping the second two and doing the same. This should give you
x^2(x - 3) + 1(x - 3). This gives you a greatest common factor of (x - 3) that you can now factor out.
(x - 3)(x^2 + 1). And you are done.
