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find m such that x+2 is the factor of 3x^3+10x^2+mx+ 14
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The Remainder Theorem states that (x+2) is the factor of p(x) = 3x^3+10x^2+mx+ 14 if and only is the number -2 is the root of the polynomial p(x).
So, (x+2) is the factor of p(x) if and only if p(-2) = 0.
Therefore, to determine "m", substitute -2 instead of x into the polynomial and equate it to zero:
3*(-2)^3 + 1-*(-2)^2 + m*(-2) + 1 = 0.
It gives you an equation to determine m.
Solve it for m. It will be your answer.
For the Remainder Theorem see the lesson
- Divisibility of polynomial f(x) by binomial x-a
in this site.