Factorisation of Polynomials

Factorize the given algebraic expression by finding common factors:

$2+14x$

Factorize the given algebraic expression:

$16xyz(x+y)$

Factorize the given algebraic expression:

$5x-20y$

Factorize the given algebraic expression:

$14m{n}^2(2m-n)$

Factorize the given algebraic expression:

$12x^{2}y\left(x+2\right)$

Factorize the quadratic equation $2x^2-7x+3=0$, by the method of completing the square.

Factorise the following: $6\sqrt{3}{\mathrm{x}}^2-47\mathrm{x}+5\sqrt{3}$ 

For what value of $a$ is the polynomial $(2x^3+a{x}^2+11x+a+3)$ exactly divisible by $(2x-1)$?