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