CAT 2012 Math practice questionbank - Number theory - Polynomial division, remainders : 2IIM CAT Classes, Study Material

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You are here: Home  »  CAT Practice Questions  »  Quant, Math  »  Number Theory  »  Question 6

Number Theory : Division of Polynomial

Remainders of division of a polynomial

Question

What number should be subtracted from x3 + 4x2 - 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 polynomial division math, then the remainder is f(-a).

In this case, as x + 3 divides x3 + 4x2 - 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



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