Question

If (x – 6) is a factor of x^3 + ax^2 + bx – b = 0 and a – b = 7, find the values of a and b.

Answer 1

If (x - 6) is a factor then f(6) = 0, that is 

6³ + a6² + b(6) - b = 0 

216 + 36a + 6b - b = 0 

36a + 5b = -216 -----(1)

but we have also given 

a - b = 7 -----(2)

So now solve these equation 1 and 2 you will get the answer