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Question

The polynomials ax3+4x2+3x4 and x34x+a leave the same remainder when divided by (x3).Find the value of a.
  1. 1
  2. 2
  3. 3
  4. 4


Solution

The correct option is A 1
Given polynomials:p(x)=ax3+4x2+3x4q(x)=x34x+a

Using remainder theorem, the remainders when p(x) and q(x) are divided by (x3) are p(3) and q(3) respectively.

p(3)=a×(3)3+4×(3)2+3×34p(3)=27a+41

q(3)=(3)34×3+a
q(3)=15+a

Given: The remainder is the same.p(3)=q(3)27a+41=15+a26a=26a=1

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