Solve 1-y^7=

$$1 - y ^ { 7 } =$$

Factor

$$\left(y-1\right)\left(-y^{6}-y^{5}-y^{4}-y^{3}-y^{2}-y-1\right)$$

Solution Steps

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. Polynomial -y^{6}-y^{5}-y^{4}-y^{3}-y^{2}-y-1 is not factored since it does not have any rational roots.

$$\left(y-1\right)\left(-y^{6}-y^{5}-y^{4}-y^{3}-y^{2}-y-1\right)$$

Evaluate

$$1-y^{7}$$