Sagot :
let f(x) = 4x^2 - 3x - 8 and use the Remainder Theorem,
f(a) = 4a^2 - 3a - 8 = 2
4a^2 - 3a - 10 = 0
(a-2)(4a + 5) = 0
a = 2 or a = -5/4
the 2nd is done the same way:
f(3) = 81 + 9m + 3n + 5 = 128
9m + 3n = 42
3m + n = 14
f(-1) = -3 - m - n + 5 = 4
-m-n = 2
add them:
2m = 16
m = 8 , then 24 + n = 14 ----> n = -10
so f(x) = 3x^3 + 8x^2 -10x + 5
f(3) = 81 + 72 - 30 + 5 = 12