How do you factor x3 plus 5x2 minus 16x minus 80?

Answer 1

To factorise x3 + 5x2 - 16x - 80 I note that -80 = 5 x -16 and 5 & -16 are the coefficients of x2 and x. Thus I have:

x3 + 5x2 - 16x - 80 = (x + 5)(x2 - 16)

and the second term is a difference of 2 squares, meaning I have:

x3 + 5x2 - 16x - 80 = (x + 5)(x + 4)(x - 4)