Use synthetic division to completely factor y=x^3-3x^2-10x+24 by x - 2.

(x-2) (x+3) (x-4)

Step-by-step explanation:

Given factor is x-2, so

The synthetic division table is:

The remainder zero proves that x-2 is a factor of x^ (3) - 3x^2-10x-24.

The division gives us the quotient.

(x^ (3) - 3x^2-10x-24) / (x-2) = x^2-x-12

The quotient is a quadratic equation which can easily be factorized.

= x^2-x-12

=x^2-4x+3x-12

=x^2-4x+3x-12

=x (x-4) + 3 (x-4)

= (x+3) (x-4)

So,

x^ (3) - 3x^2-10x-24 = (x-2) (x+3) (x-4)