Question

How do you factor `x^3 - 2x^2 - 5x + 10`?

Answer 1

Apply factoring by grouping to obtain

`x^3-2x^2-5x+10 = (x^2-5)(x-2)`

Explanation:

By grouping:

`x^3-2x^2-5x+10 = x^2(x-2)-5(x-2)`

`= (x^2-5)(x-2)`

We could further factor `x^2-5 = (x+sqrt(5))(x-sqrt(5))` by the difference of squares technique, however the above suffices if we only want a solution involving integers.