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Question

If 1(x 1)(x + 2)(2x + 3) can be expressed as Ax 1 + Bx + 2 + C2x + 3 then what will be the respective values of A, B and C?


A

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B

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C

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D

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Solution

The correct option is B


The approach to solve these kind of questions should be by cross checking. Let's take LCM of Ax 1 + Bx + 2 + C2x + 3 and rewrite this-

A(x + 2)(2x + 3) + B(x 1)(2x + 3) + C(x 1)(x + 2)(x 1)(x + 2)(2x + 3)

or

A(2x2 + 3x + 2x + 6) + B(2x2 + 3x 2x 3) + C(x2 + 2x x 2(x 1)(x + 2)(2x + 3)

or

x2(2A + 2B + C) + x(5A + B + C) + 6A 3B 2C(x 1)(x + 2)(2x + 3)

Now we'll compare the expression we got with the given expression. That is, comparing the numerator of the above expression with numerator of 1(x 1)(x + 2)(2x + 3)

So, 2A + 2B + C = 0 (coefficient of x2 = 0)

5A + B + C = 0 (coefficient of x = 0)

6A - 3B - 2C = 1

We have three equations and three variables. On solving these equations we get A = 115, B = 13, C = 45

We can also put the values given in the options and check which option satisfies these 3 equations.


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