Solve y^6*y^4+y^5

$$y ^ { 6 } \times y ^ { 4 } + y ^ { 5 }$$

Factor

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

Solution Steps

Factor out y^{5}.

$$y^{5}\left(yy^{4}+1\right)$$

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.

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

Evaluate

$$y^{10}+y^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$y^{10}+y^{5}$$