Solve 10u+20-10u^6

$$10 u + 20 - 10 u ^ { 6 }$$

Factor

$$10\left(u+1\right)\left(2-u+u^{2}-u^{3}+u^{4}-u^{5}\right)$$

Solution Steps

Factor out 10.

$$10\left(u+2-u^{6}\right)$$

Consider u+2-u^{6}. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 2 and q divides the leading coefficient -1. One such root is -1. Factor the polynomial by dividing it by u+1.

$$\left(u+1\right)\left(-u^{5}+u^{4}-u^{3}+u^{2}-u+2\right)$$

Rewrite the complete factored expression. Polynomial -u^{5}+u^{4}-u^{3}+u^{2}-u+2 is not factored since it does not have any rational roots.

$$10\left(u+1\right)\left(-u^{5}+u^{4}-u^{3}+u^{2}-u+2\right)$$

Evaluate

$$10\left(2+u-u^{6}\right)$$