TS EAMCET 4 May 2018 Shift 1 Solved Paper

Consider the expression.

x4+x3+2x2−2x+1

x3+x2

=P(x)+

A

x

+

B

x2

+

C

x+1

Let P(x)=x
The above expression can now be simplified as,

x4+x3+2x2−2x+1

x3+x2

=x+

A

x

+

B

x2

+

C

x+1

x+

2x2−2x+1

x3+x2

=x+

A

x

+

B

x2

+

C

x+1

2x2−2x+1

x3+x2

=

A(x)(x+1)+B(x+1)+Cx2

x3+x2

2x2−2x+1=A(x)(x+1) +B(x+1)+Cx2
Compare the coefficient of like terms,
A+C=2……. (I)
A+B=−2 ……. (II)
And,
B=1 ……. (III)
Therefore,
A=−3
B=1
C=5
Hence,
A+B+C=3
And P(x)=x
Therefore,
A+B+C=P(3)