maths
posted by kusum .
ifx^3+mx^2+nx+6 has x2 as a factor and leaves remainder 3 when divided by x3, find the values of m and n.

let f(x) = x^3 + mx^2 + nx + 6
given:
f(2) = 0
= 8 + 4m + 2n + 6 = 0 > 2m + n = 7
given: f(3) = 3
= 27 + 9m + 3n + 6 = 3  3m + n = 10
subtract the two equations to get : m = 3
sub that into 2m+n=7
6 + n = 7
n = 1
m= 3, n = 1