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Question 29647: When a polynomial P(x) is divided by x-1, the remainder is 5. When P(x) is divided by x-2, the remainder is 2. Find the Remainder when P(x) is divided by (x-1)(x-2).
THANKS...PLEASE ANSWER THIS!
-Rebecca
Answer by ikdeep(226)   (Show Source):
You can put this solution on YOUR website! We have formula i.e.
Divident = divisor * quotient + remainder
Now according to first condition i.e. When a polynomial P(x) is divided by x-1, the remainder is 5...we get the equation....
divident i.e p(x) = (x-1)* quotient + 5
let the quotient = q
so ...divident = (x-1)* q + 5
divident = qx - 1q + 5....(1)
Now according to second condition i.e. When P(x) is divided by x-2, the remainder is 2...we get the equation....
divident i.e p(x) = (x-2)* quotient + 2
again on solving this equation we get ....
divident = qx - 2q + 2....(1).....
Also we know that divident or p(x) is same in both equation,,so we get...
qx - 2q + 2 = qx - q1 + 5
- 2q + 2 = - q1 + 5 (qx on both side wolud be eliminated).
-2q + 1q = 5 - 2
-q = 3
or q = -3
therefore we get the value of quotient = -3 ...
now on substituting the value of q either in (1) or (2), would give the value of divident or p(x)...and we get
divident = qx - 1q + 5....(1)
= -3x - (-3) + 5
= -3x + 3 + 5
= -3x + 8....p(x)...
Here comes the solution of half of your question..
Now, when we see the 2nd half of the question, where you have written "Find the Remainder when P(x) is divided by (x-1)(x-2)."
I think that this is an incorrect statement as if you see carefully you might notice that here divident or P(x) i.e -3x + 8 (which we calculated above) is smaller than (x-1)(x-2) and such a division will not give a logical answer .
Instead, of this, I think (x-1)(x-2) is to be divided by P(x)...
so, check the question and contact me again ...
hope this will help you
Please feel free to revert back for any further queries.
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