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Spot the mistake in the following factorisation:

$3 x 2 − 4 − 4 x = 3 x 2 − 4 x − 4 = 3 x 2 + 6 x − 2 x − 4 = 3 x (x + 2) − 2 (x + 2) = (x + 2) (3 x − 2)$

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Line 1

Line 2

Line 3

Line 4

answer is B.

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Detailed Solution

Given a factorization of polynomial

3 x 2 − 4 − 4 x = 3 x 2 − 4 x − 4 = 3 x 2 + 6 x − 2 x − 4 = 3 x (x + 2) − 2 (x + 2) = (x + 2) (3 x − 2)

Let us find at which step error is present
Follow the concept of mid term explicit.
In step

3 x 2 + 6 x − 2 x − 4

we have

6 x − 2 x = 4 x

but in step one we have

− 4 x

So there is mistake in this line.
The correct step must be

3 x 2 − 6 x + 2 x − 4

So, there is mistake in

3 x 2 + 6 x − 2 x − 4

which is in line 2.
Hence the correct option is 2.

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