Comment 1: Try rational roots formed by that +3 and that +4:
For example:
Some of the POSSIBLE rational roots include plus or minus 4/3, 4/1, 2/3, 2/1, and so on. Typically one would choose one of these POSSIBLE roots to start with and divide using synthetic division. If there is only a zero remainder, that would be an indication that the chosen possible root actually is a rational root of 4x^3-9x^2-10x+3=0.
Let's try the possible rational root 3/4. This was strictly a random choice.
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3/4 / 4 -2 -10 3
3 3/4
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4 1 -9 1/4 (not finished, but this info is enough to warrant
rejecting 3/4 as a rational root; there is a non-
zero remainder here.)
check out other possibilities, such as -1/4, -1/2, etc., until you find a divisor that leaves no remainder.