The values of m and n are -29/3 and 40/3 respectively
A polynomial is a function that has a leading degree of 2 and greater. Given the polynomial
P(x) = 2x^3 + mx^2 + nx – 2
If it is divided by x – 3, the remainder is 4 and divided by x – 2, the remainder is 2, hence;
4 = 2(3)^3 + 9m + 3n - 2
4 = 54 + 9m + 3n - 3
9m + 3n = -47
Similarly
2 = 2(2)^3 + 4m + 2n - 2
4m + 2n = -12
Solve simultaneously
9m + 3n = -47 * 2
4m + 2n = -12 * 3
______________
18m + 6n = -94
12m + 6n = -36
Subtract
6m = -58
m = -58/6 = -29/3
For the value of n
4m + 2n = -12
2m + n = -6
2(-29/3) + n = -6
n = -6 + 58/3
n = 40/3
Hence the values of m and n are -29/3 and 40/3 respectively
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