Factor
\left(x+1\right)\left(x^{6}-x^{5}+24x^{4}-24x^{3}+24x^{2}-24x+25\right)
Evaluate
x^{7}+23x^{5}+x+25
Graph
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\left(x+1\right)\left(x^{6}-x^{5}+24x^{4}-24x^{3}+24x^{2}-24x+25\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 25 and q divides the leading coefficient 1. One such root is -1. Factor the polynomial by dividing it by x+1. Polynomial x^{6}-x^{5}+24x^{4}-24x^{3}+24x^{2}-24x+25 is not factored since it does not have any rational roots.
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