Question

Given f(x) = x³-4x²+ax+b is divisible by (x²-3x+2) . the value of a-b = ??????

Answer 1

F(x) = x³-4x²+ax+b
x² - 3x + 2 = (x - 2)(x - 1)

f(2) = (2)³ - 4(2)² + 2a + b
0 = 8 - 16 + 2a + b
0 = -8 + 2a + b
8 = 2a + b

f(1) = (1)³ - 4(1)² + 1a + b
0 = 1 - 4 + a + b
0 = -3 + a + b
3 = a + b

*
2a + b = 8
a + b = 3
---------------- - 
a = 5

* 
a + b = 3
5 + b = 3
b = 3 - 5
= -2 

* a - b = ?
= 5 - (-2) 
= 5 + 2
= 7