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
If
is
a root,
is
a factor.
constant:
hence
The quadratic in the brackets can now be factorised by
inspection:
Example:
If
is
a root of
factorise
If
is
a root,
is
a factor.
constant:
hence
The quadratic in the brackets can now be factorised by
inspection:
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