Factors of a polynomial can divide it without leaving remainder. The other factor of
is given by Option D : ![3x + 2](https://tex.z-dn.net/?f=3x%20%2B%202)
<h3>How to factorize a polynomial?</h3>
Let the polynomial A(x) has one factor f(x).
Then, it means, we have:
![\dfrac{A(x)}{f(x)} = g(x)](https://tex.z-dn.net/?f=%5Cdfrac%7BA%28x%29%7D%7Bf%28x%29%7D%20%3D%20g%28x%29)
Thus, A(x) can be written as ![A(x) = f(x) \times g(x)](https://tex.z-dn.net/?f=A%28x%29%20%3D%20f%28x%29%20%5Ctimes%20g%28x%29)
Thus, the other factor of that polynomial is
![g(x) = \dfrac{A(x)}{f(x)}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cdfrac%7BA%28x%29%7D%7Bf%28x%29%7D)
For given case, the polynomial
is
![A(x) = 6x^2 - 7x + 2](https://tex.z-dn.net/?f=A%28x%29%20%3D%206x%5E2%20-%207x%20%2B%202)
Its one factor f(x) is given ![f(x) = 2x - 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%202x%20-%201)
Thus, its second factor is obtained as:
![g(x) = \dfrac{A(x)}{f(x)} = \dfrac{6x^2 - 7x + 2}{(2x - 1)} = \dfrac{6x^2 -4x -3x - 2}{2x - 1}\\\\g(x) = \dfrac{2x(3x + 2) - 1(3x + 2)}{2x - 1} = \dfrac{(2x - 1)(3x + 2)}{2x - 1}\\\\g(x) = (3x + 2)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cdfrac%7BA%28x%29%7D%7Bf%28x%29%7D%20%3D%20%5Cdfrac%7B6x%5E2%20-%207x%20%2B%202%7D%7B%282x%20-%201%29%7D%20%20%3D%20%5Cdfrac%7B6x%5E2%20-4x%20-3x%20-%202%7D%7B2x%20-%201%7D%5C%5C%5C%5Cg%28x%29%20%3D%20%5Cdfrac%7B2x%283x%20%2B%202%29%20-%201%283x%20%2B%202%29%7D%7B2x%20-%201%7D%20%3D%20%5Cdfrac%7B%282x%20-%201%29%283x%20%2B%202%29%7D%7B2x%20-%201%7D%5C%5C%5C%5Cg%28x%29%20%3D%20%283x%20%2B%202%29)
Thus, the second factor of the given polynomial is
Option D : ![3x + 2](https://tex.z-dn.net/?f=3x%20%2B%202)
Learn more about factors of polynomials here:
brainly.com/question/16078564