Am a newbie with additional math. When factorising polynomials with a constant of zero using the remainder theorem, the only method I can think of at the moment is random hit and miss since we have two unknown factors (for a cubic).
Please advise how, for a polynomial such as $f(x)= x^3-x^2-2x$, I should go about finding the other two factors (not x), as efficiently as possible?
Many thanks.
$$f(x)= x^3-x^2-2x=x(x^2-x-2)=x(x-2)(x+1)$$
The other factors are $x-2$ and $x+1$ because $x=2$ and $x=-1$ make $f(x)=0.$
Thus the remainder of your polynomial in dividing by $x+1$ and $x-2$ is zero.