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Factorise the expression $11 x 2 − 54 x + 63$ .

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x − 3 11 x − 21

x + 3 11 x − 21

x + 3 11 x + 21

None of these

answer is A.

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Detailed Solution

Given expression is

11 x 2 − 54 x + 63

.
To factorise the given expression, taking the product of the coefficient of

x 2

with the constant term,

11 × 63 = 693

Now, finding the factors of 693 and treat them as the coefficient of x.

693 = 33 × 21

Now, adding the factors,

33 + 21 = 54

So, the expression can be written as:

11 x 2 − 54 x + 63 = 11 x 2 − 33 + 21 x + 63 ⇒ 11 x 2 − 54 x + 63 = 11 x 2 − 33 x − 21 x + 63 ⇒ 11 x 2 − 54 x + 63 = 11 x x − 3 − 21 x − 3 ⇒ 11 x 2 − 54 x + 63 = x − 3 11 x − 21

Therefore, the factorisation of the given expression is

x − 3 11 x − 21

.
Hence, option 1 is correct.

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