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Factorise the expression $7 x 2 − 19 x − 6$ .

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x − 3 7 x + 2

x − 3 7 x − 2

x + 3 7 x + 2

None of these

answer is A.

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Detailed Solution

Given expression is

7 x 2 − 19 x − 6

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

x 2

with the constant term,

7 × (− 6) = − 42

Now, finding the factors of

42

and treat them as the coefficient of x.

42 = 2 × 21

Now, subtracting the factors,

2 − 21 = − 19

So, the expression can be written as:

7 x 2 − 19 x − 6 = 7 x 2 − 21 − 2 x − 6 ⇒ 7 x 2 − 19 x − 6 = 7 x 2 − 21 x + 2 x − 6 ⇒ 7 x 2 − 19 x − 6 = 7 x x − 3 + 2 x − 3 ⇒ 7 x 2 − 19 x − 6 = x − 3 7 x + 2

Therefore, the factors of the given expression are

x − 3 7 x + 2

.
Hence, option 1 is correct.

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