Question

Show that (x+4) is a factor of x^3+5x^2-2x-24. Then find the remaining factors of the polynomial.

Answer 1

Given the polynomial:

$x^3+5x^2-2x-24$

We need to prove that (x+4) is a factor of the polynomial. Then, using the long division for polynomials:

Then, we showed that (x+4) is a factor of the polynomial, and the other factor is:

$x^2+x-6=(x+3)(x-2)$

Finally, the factored form of the polynomial is:

$x^3+5x^2-2x-24=(x+4)(x+3)(x-2)$