Question

How do you factor the expression `r^3 - 3r^2 - 54r`?

Answer 1

`r(r-9)(r+6)`

Explanation:

`r^3 - 3r^2 - 54r = = r(r^2 - 3r - 54)`

`54 = 54 * 1 = 27 * 2 = 6 * 9`.

You can thus say that

`r^2 - 3r - 54 = r^2 + 6r - 9r - 54`

`r(r + 6) - 9(r + 6) = (r-9)(r+6)`

Therefore, the original expression can be factored as

`r * (r-9)(r+6)`