Question 229599
Factor:
{{{b^3-2b^2-63b}}} First, since each term has common factor of b, a b can be factored.
{{{b(b^2-2b-63)}}} 
Now look at the constant term (-63) and see what its factors are:
{{{-63 = 3(-21)}}}
{{{-63 = -3(21)}}}
{{{-63 = 7(-9)}}}
{{{-63 = -7(9)}}}
Now you need the pair of factors from the above list whose sum is -2 (the coefficient of the center term of the trinomial.
A quick look will show that the pair that meets this requirement is {{{7(-9)}}} because {{{7+(-9) = -2}}}. Now you can finish the factoring process.
{{{highlight(b^3-2b^2-63b = b(b+7)(b-9))}}}