Math CentralQuandaries & Queries


Question from Tehmas, a student:

Determine the values of m and n so that the polynomials 2x^3+mx^2+nx-3 and
x^3-3mx^2 +2nx +4 are both divisible by x-2.

Hi Tehmas,

If $x - 2$ divides a polynomial $p(x)$ then there is another polynomial $q(x)$ so that $p(x) = (x - 2) q(x).$ Substituting $x = 2$ into this equation gives $p(2) = (2 - 2) q(2) = 0$ and hence substitution of $x = 2$ into each of the polynomials in your problem yields a value of $0.$

Can you complete the problem now?

Write back of you need more help,

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