Solve 13n^2+11n-2n^4)+(-8n^2-3n-6n^4)

$$13 n ^ { 2 } + 11 n - 2 n ^ { 4 } ) + ( - 8 n ^ { 2 } - 3 n - 6 n ^ { 4 } )$$

Factor

$$n\left(n+1\right)\left(11+2n-2n^{2}\right)$$

Solution Steps

Factor out n.

$$n\left(13n+11-2n^{3}\right)$$

Consider 13n+11-2n^{3}. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 11 and q divides the leading coefficient -2. One such root is -1. Factor the polynomial by dividing it by n+1.

$$\left(n+1\right)\left(-2n^{2}+2n+11\right)$$

Rewrite the complete factored expression. Polynomial -2n^{2}+2n+11 is not factored since it does not have any rational roots.

$$n\left(n+1\right)\left(-2n^{2}+2n+11\right)$$

Evaluate

$$n\left(11+13n-2n^{3}\right)$$