Question

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!

Answer 1

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

Answer 2

So what is the answer?

Answer 3

Continuing from the partial solution from 10 years ago, except I've fixed the mistake in getting to one of the equations.
(1) -6m + 2n + 6
(2) 4m + 2n + 13

Proceed with elimination:
-6m + 2n + 6 = 4m + 2n + 13
-6m + 6 = 4m + 13
10m = -7
m = -0.7

Proceed with substitution:
(2) 4m + 2n + 13
4(-0.7) + 2n + 13 = 0
-2.8 + 2n + 13 = 0
2n = -10.2
n = -5.1

Hopefully this goes through the solution well enough.
(Also, it's pretty crazy that the first part of this solution was done over 10 years ago... collaboration across time!!!)

Answer 4

How are you getting -6m + 2n + 6 as the one equation? I keep on getting -12m-4n+12. Am I missing a step or just doing it wrong?