Factor
x\left(x-7\right)\left(-x^{2}-7x-49\right)
Evaluate
x\left(343-x^{3}\right)
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x\left(343-x^{3}\right)
Factor out x.
\left(x-7\right)\left(-x^{2}-7x-49\right)
Consider 343-x^{3}. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 343 and q divides the leading coefficient -1. One such root is 7. Factor the polynomial by dividing it by x-7.
x\left(x-7\right)\left(-x^{2}-7x-49\right)
Rewrite the complete factored expression. Polynomial -x^{2}-7x-49 is not factored since it does not have any rational roots.
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