Let f(x) = ax^3 + bx^2 + 3x – 4. If f(x) is divided by (x – 2), the remainder is 2. When it is divided by (x – 1), the remainder is -2. Find a and b.
f(2) = 2
f(1) = -2
8a + 4b + 6 - 4 = 2
a + b + 3 - 4 = -2
8a + 4b = 0
a + b = -1
so, b = -2a
a = 1
b = -2
f(x) = x^3 - 2x^2 + 3x - 4