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