Question 1052047
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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.
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For the Remainder Theorem see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Divisibility-of-polynomial-f%28x%29-by-binomial-x-a.lesson>Divisibility of polynomial f(x) by binomial x-a</A>

in this site.