Question

How do you factor `x^3-3x^2-81x+243`?

Answer 1

`=(x-3)(x+9)(x-9)`

Explanation:

If an expression has 4 more more terms, group them in pairs (or threes) first - making sure there is + sign between the groups.

`(x^3 - 3x^2) + (-81x +243) " look for a common factor"`

`=x^2(x -3) -81(x -3)`

Note that -81 was used as a common factor so the sign in the second bracket changed.
`= (x -3)(x^2-81) " difference of squares"`

`=(x-3)(x+9)(x-9)`