Factor
5\left(y+1\right)\left(y^{6}-y^{5}+y^{4}-y^{3}+y^{2}-y+1\right)
Evaluate
5\left(y^{7}+1\right)
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5\left(y^{7}+1\right)
Factor out 5.
\left(y+1\right)\left(y^{6}-y^{5}+y^{4}-y^{3}+y^{2}-y+1\right)
Consider y^{7}+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.
5\left(y+1\right)\left(y^{6}-y^{5}+y^{4}-y^{3}+y^{2}-y+1\right)
Rewrite the complete factored expression. Polynomial y^{6}-y^{5}+y^{4}-y^{3}+y^{2}-y+1 is not factored since it does not have any rational roots.
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\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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