Factorising $x^3+2x^2-c^3-2c^2$

Question

How would you go about factorising this?

I mean how would you go from this first line to the next line?

(what step goes on between these lines?)

$x^3+2x^2 -c^3-2c^2$

$= (x-c)(c^2+cx+2c+x^2+2x)$

Answer 1

First see that $c$ is a root of the polynomial in $x$ you have (that is: $c^3 + 2c^2 - c^3 -2c^2 = 0$). Therefore you can factor $(x-c)$. Then using Horner's algorithm you get your factorisation.

Answer 2

$$(x^3-c^3)+2(x^2-c^2)=(x-c)(x^2+cx+c^2)+2(x-c)(x+c)$$ $$(x-c)(x^2+cx+c^2+2(x+c))=(x-c)(x^2+(c+2)x+c^2+2c)$$