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Factorize the polynomial expression $7 x 2 − 19 x − 6$ , and choose the option which represents the factored form correctly.

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(x – 3) (7x - 2)

(x - 3) (7x + 2)

(7x – 3) (x + 2)

(x + 3) (7x - 2)

answer is A.

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Detailed Solution

The given quadratic equation

7 x 2 − 19 x − 6

can be written in the standard form 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 find the factors of product, i.e.,

− 42

in such a way 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 difference, i.e.,

21 − 2 = 19

is the middle term of the given equation.
Now, we 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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