Number Theory : Division of Polynomial
Remainders of division of a polynomial
Question
What number should be subtracted from x
3 + 4x
2 - 7x + 12 if it is to be perfectly divisible by x + 3?
(1) 42
(2) 39
(3) 13
(4) None of these
Correct Choice is
(1) and Correct Answer is
42
Explanatory Answer
According to remainder theorem when

, then the remainder is f(-a).
In this case, as x + 3 divides x
3 + 4x
2 - 7x + 12 - k perfectly (k being the number to be subtracted), the remainder is 0 when the value of x is substituted by -3.
i.e., (-3)
3 + 4(-3)
2 - 7(-3) + 12 - k = 0
or -27 + 36 + 21 + 12 = k
or k = 42
CAT Practice Questions and Answers : Listed Topicwise
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Number Theory |