Express the polynomial x^3+x^2-14x-24 as a product of three linear factors.

Firstly, use the factor theorem to determine one factor. Substitute factors of 24 into the equation, beginning at plus or minus 1 and then increasing. The first factor found will be -2, therefore (x+2) is a factor.

Using polynomial division, we find that (x³ + x² -14x-24)/(x+2) = x² - x -12. This can be easily factorised into (x-4)(x+3), so the final answer is (x-4)(x+3)(x+2).

This can be checked by expanding the brackets.