Factor
3\left(w-1\right)\left(3w^{4}+7w^{3}+7w^{2}+7w+7\right)
Evaluate
9w^{5}+12w^{4}-21
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3\left(3w^{5}+4w^{4}-7\right)
Factor out 3.
\left(w-1\right)\left(3w^{4}+7w^{3}+7w^{2}+7w+7\right)
Consider 3w^{5}+4w^{4}-7. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -7 and q divides the leading coefficient 3. One such root is 1. Factor the polynomial by dividing it by w-1.
3\left(w-1\right)\left(3w^{4}+7w^{3}+7w^{2}+7w+7\right)
Rewrite the complete factored expression. Polynomial 3w^{4}+7w^{3}+7w^{2}+7w+7 is not factored since it does not have any rational roots.
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