Solve 7y^6+7y

$$7 { y }^{ 6 } +7y$$

Factor

$$7y\left(y+1\right)\left(y^{4}-y^{3}+y^{2}-y+1\right)$$

Solution Steps

Factor out 7.

$$7\left(y^{6}+y\right)$$

Consider y^{6}+y. Factor out y.

$$y\left(y^{5}+1\right)$$

Consider y^{5}+1. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 1 and q divides the leading coefficient 1. One such root is -1. Factor the polynomial by dividing it by y+1.

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

Rewrite the complete factored expression. Polynomial y^{4}-y^{3}+y^{2}-y+1 is not factored since it does not have any rational roots.

$$7y\left(y+1\right)\left(y^{4}-y^{3}+y^{2}-y+1\right)$$

Evaluate

$$7y\left(y^{5}+1\right)$$