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Determine the values of a M and N , so that the polynomial 2x^3+mx^2+nx-3 and X^3-3mx^2+2nx+4 are both divisible by x-2.

I am so lost, i do not know how to start this problem! please help i have a test soon!

• MATH grade 12 -

Just change the variable x with the value x = 2. So, we get:
f(x) = 2x^3 + mx^2 + nx - 3
f(2) = 0 = 2(8) + 4m + 2n - 3
0 = 13 + 4m + 2n. ..(1)

g(x) = 3mx^2 + 2nx + 4
g(2) = 0 = 12m + 4n + 4
0 = 6m + 2n + 2. ..(2)

Using elimination and substitution for both equation (1) and (2), you'll get the values of m and n

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