Solve y^7-128

$$y ^ { 7 } - 128$$

Factor

$$\left(y-2\right)\left(y^{6}+2y^{5}+4y^{4}+8y^{3}+16y^{2}+32y+64\right)$$

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 -128 and q divides the leading coefficient 1. One such root is 2. Factor the polynomial by dividing it by y-2. Polynomial y^{6}+2y^{5}+4y^{4}+8y^{3}+16y^{2}+32y+64 is not factored since it does not have any rational roots.

$$\left(y-2\right)\left(y^{6}+2y^{5}+4y^{4}+8y^{3}+16y^{2}+32y+64\right)$$

Evaluate

$$y^{7}-128$$