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. (4 marks)
f(x) divided by x-2 leaves remainder of 2 ---> f(2) = 2
f(x) divided by x-1 leaves a remainder of -2 --> f(1) = -2
f(2) = 8a + 4b + 6 - 4 = 2
8a + 4b = 0
2a + b = 0
f(1) = a + b + 3-4 = -2
a + b = -1
subtract them:
a = 1
back in a+b=-1
1+b = -1
b = -2
a = 1 , b = -2
check my arithmetic