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Which of the following are the factors of the polynomial $4 (a + b) − 6 (a + b) 2$ containing $a and b$ ?

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(a − b) and (2 − 3 a − 3 b)

(a + b) and (2 − 3 a − 3 b)

(a + b) and (2 − 3 a + 3 b)

(a + b) and (2 + 3 a − 3 b)

answer is A.

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Detailed Solution

The given polynomial is

4 (a + b) − 6 (a + b) 2 .

Taking out the common terms from the given polynomial, we get

2 (a + b) [2 − 3 (a + b)] .

Solving the term in the bracket, we get

2 (a + b) (2 − 3 a − 3 b) .

There are only two factors containing

a and b

(a + b)

and

(2 − 3 a − 3 b) .

Hence, option (1) is correct.

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