Question

Factorize the polynomial expression $4x^2-3x-7$

• A. $(4x-7)(x+1)$
• B. $(4x-7)(x-1)$
• C. $(4x+7)(x+1)$
• D. $(4x+7)(x-1)$

Answer 1

The correct option is A $(4x-7)(x+1)$

Given a polynomial expression $4x^2-3x-7$.

Factorizing this polynomial by splitting the middle term:

Product of $4x^2$ and $-7$
$=4x^2\times (-7)$
$=-28x^2$

We need to find two numbers whose product is $-28x^2$ and sum is $-3x$.
The numbers are $4x$ and $-7x$. ($\because -7x+4x=-3x$)

Now, splitting the middle term:
$4x^2\underset{–}{-3x}-7$
$=4x^2-7x+4x-7$

Taking ${}^{\prime }{x}^{\prime }$ common from the first two terms and $1$ from the last two terms:
$=x(4x-7)+1(4x-7)$

Since, $(4x-7)$ is the common factor in both the terms, we can take $(4x-7)$ as the common factor:
$=(4x-7)(x+1)$

$4x^2-3x-7=(4x-7)(x+1)$

The factorization of the polynomial expression $4x^2-3x-7$ is $(4x-7)(x+1)$. Therefore, option (a.) is the correct answer.