$a)$ $6x^2 - 11x + 3$

$= 6x^2 - 9x - 2x + 3$

$= 3x(2x - 3) - (2x - 3)$

$= (2x - 3)(3x - 1)$

 

$b)$ $3x^2 + 3x - 27$

$= 3(x^2 + x - 9)$

$= 3\left[\left(x + \frac{1}{2}\right)^2 - \frac{37}{4}\right]$

$= 3\left(x + \frac{1 - \sqrt{37}}{2}\right)\left(x + \frac{1 + \sqrt{37}}{2}\right)$

 

$c)$ $2x^2 - 5xy - 3y^2$ 

$= 2x^2 - 6xy + xy - 3y^2$

$= 2x(x - 3y) + y(x - 3y)$

$= (x - 3y)(2x + y)$

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