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Factorise $7 x 2 − 19 x − 6$ and select the option which represents its factored form from the given options below.

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(x − 3) (7 x + 2)

(x − 2) (7 x + 3)

(x + 2) (7 x − 3)

(x + 3) (7 x − 2)

answer is A.

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Detailed Solution

The given quadratic equation is as follows,

7 x 2 − 19 x − 6

.
Now, it is of the form

a x 2 + b x + c

, where a = 7, b = -19 and c = -6. In order to factorise these types of equations, we need to find two factors, say p and q such that the following two conditions are satisfied,

a c = p q

p + q = b

According to the above conditions, the product of first and last constant term of the expression will be

7 × (− 6) = − 42

.
Next, we will have to find the factors of product, i.e.,

− 42

, in such a way that their sum or difference is equal to the middle term. So, we have the factors as

− 21 × 2 = − 42

, which is the product of the first and last terms of the equation, while their sum, i.e.,

− 21 + 2 = − 19

is the middle term.
Now, we will factorise the expression using the factors and splitting the middle term as follows,

7 x 2 − 19 x − 6 = 7 x 2 − 21 x + 2 x − 6 = 7 x (x − 3) + 2 (x − 3) = (x − 3) (7 x + 2)

So, the factored form of

7 x 2 − 19 x − 6

(x − 3) (7 x + 2)

.
Hence, the correct option is (1).

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