Solve x^3+8x^2+3x^2+24x-x-8

$$x ^ { 3 } + 8 x ^ { 2 } + 3 x ^ { 2 } + 24 x - x - 8$$

Evaluate

$$\left(x+8\right)\left(x^{2}+3x-1\right)$$

Solution Steps

Combine 8x^{2} and 3x^{2} to get 11x^{2}.

$$x^{3}+11x^{2}+24x-x-8$$

Combine 24x and -x to get 23x.

$$x^{3}+11x^{2}+23x-8$$

Factor

$$\left(x+8\right)\left(x^{2}+3x-1\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{3}+11x^{2}+23x-8$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -8 and q divides the leading coefficient 1. One such root is -8. Factor the polynomial by dividing it by x+8. Polynomial x^{2}+3x-1 is not factored since it does not have any rational roots.

$$\left(x+8\right)\left(x^{2}+3x-1\right)$$