We know how to factorise quadratic equations but it is much harder to factorise cubic because in general there is no easy to see relationship between the coefficients. If we are given a factor or a root however, the problem becomes much more solvable. We can write the cubic expression as a product of a linear factor with a quadratic expression, expand the brackets and simplify and solve for the coefficients.
Example:
If
is a root of
factorise
Ifis a root,
is a factor.
constant:
hence
The quadratic in the brackets can now be factorised by inspection:
Example:
If
is a root offactorise
Ifis a root,
is a factor.
constant:
hence
The quadratic in the brackets can now be factorised by inspection: