Given one factor of the polynomial, factor the polynomial completely.

f(x) = x^3 - 4x^2 - 7x + 10; x - 5

The factors are (x  - 1)(x - 5)(x + 2).

Step-by-step explanation:

Long division:

x - 5 )x^3 - 4x^2 - 7x + 10( x^2 + x - 2 < Quotient.

        x^3 - 5x^2

                   x^2 - 7x

                    x^2 - 5x

                           - 2x + 10

                            -2x + 10

x^ 2 + x - 2 = (x + 2)(x - 1).