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Question

If x3(2x−1)(x+2)(x−3)= A+B(2x−1)+C(x+2)+D(x−3) then A=

A
12
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B
150
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C
825
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D
2725
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Solution

The correct option is C 12
x3(2x1)(x+2)(x3)= A+B(2x1)+C(x+2)+D(x3)
Cross multiplying,
x3=A(2x1)(x+2)(x3)+B(x+2)(x3)+C(2x1)(x3)+D(2x1)(x+2)
Substitute x=1/2 both sides
1/8=B(5/2)(5/2)B=1/50
Substitute x=2 both sides,
8=C(5)(5)C=8/25
Substitute =3 both sides,
27=D(5)(5)D=27/25
Now put x=0 both sides,
0=6A6B+3C2D
6A=6B3C+2D=3/25+24/25+54/25=3A=1/2
Hence option 'A' is correct choice.

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