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Polynomial Divisions (Posted on 2007-08-13) Difficulty: 2 of 5
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?

See The Solution Submitted by Brian Smith    
Rating: 3.2000 (5 votes)

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Solution Solution Comment 3 of 3 |

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.


  Posted by K Sengupta on 2007-08-21 11:29:36
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