A polynomial P(x) is divisible by x-5. If P(x) is divided by x-2 then the quotient is polynomial Q(x) and the remainder is 30. What is the remainder when Q(x) is divided by x-5?
By the conditions of the problem, we have:
(I)(x-5) divides P(x)
(II) P(x) = (x-2)*Q(x) + 30
From (I), we have P(5) = 0 .......(*)
Accordingly, substituting x= 5 in (II), we obtain:
P(5) = 3*Q(5) + 30
Or, 0 = 3*Q(5) + 30 (from (*))
Or, 3*Q(5) = -30, giving:
Or, Q(5) = -10
Thus, the required remainder when Q(x) is divided by x-5 is -10.