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Question

If 3x+2(x+1)(2x2+3)=A(x+1)+Bx+C2x2+3, then A+C-B=


A

0

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B

2

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C

3

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D

5

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Solution

The correct option is B

2


Step 1. Find the value of A+C-B:

Given, 3x+2(x+1)(2x2+3)=Ax+1+Bx+C2x2+3

3x+2=A(2x2+3)+(Bx+C)(x+1)

Put x=1

3(-1)+2=A(2(1)+3)+(B(-1)+C)(-1+1)

-3+2=A(5)

-1=A(5)

-15=A

Step 2. On comparing the coefficients, we get

2A+B=0

B=-2A

=25

3A+C=2

C=2+35

=135

A+CB=(15)+13525=2

Hence, Option ‘(B)’ is Correct.


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