Solve 9x+18-6x^2-12x-x^3-2x^2

$$9 x + 18 - 6 x ^ { 2 } - 12 x - x ^ { 3 } - 2 x ^ { 2 }$$

Evaluate

$$\left(x+2\right)\left(9-6x-x^{2}\right)$$

Solution Steps

Combine 9x and -12x to get -3x.

$$-3x+18-6x^{2}-x^{3}-2x^{2}$$

Combine -6x^{2} and -2x^{2} to get -8x^{2}.

$$-3x+18-8x^{2}-x^{3}$$

Factor

$$\left(x+2\right)\left(9-6x-x^{2}\right)$$

Solution Steps

Multiply and combine like terms.

$$-x^{3}-8x^{2}-3x+18$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 18 and q divides the leading coefficient -1. One such root is -2. Factor the polynomial by dividing it by x+2. Polynomial -x^{2}-6x+9 is not factored since it does not have any rational roots.

$$\left(x+2\right)\left(-x^{2}-6x+9\right)$$