Review Rational Roots Theorem. The possible roots to check, helpful for factoring, are the plusses and minuses of 1, 3, 1/2, 3/2; and you might expect as many as up to five complex roots.
Setup your first-root synthetic divisions this way:
ROOT | 2 4 -5 0 0 3
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Because you must account for all lower degree of the variable.
You will find that NONE of the possible rational roots checked will work; meaning remainder in the synthetic divisions will be NONZERO. The factor is the PRIME factor.
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I did not actually perform the divisions. I used the graphing feature of Google Chrome browser.