$a)f\left(x\right)=2x^2-6x=2x\left(x-3\right)$

$b)f\left(x\right)=\frac{1}{3}{x}^2+2x=x\left(\frac{1}{3}x+2\right)$

$c)f\left(x\right)=-x^2-2x+15=\dots$

$\Delta ={\left(-2\right)}^2-4\cdot \left(-1\right)\cdot 15=$

$=4+60=64$

$\sqrt{\Delta }=\sqrt{64}=8$

$x_1=\frac{2-8}{-2}=\frac{-6}{-2}=3$

$x_2=\frac{2+8}{-2}=\frac{10}{-2}=-5$

$\dots =-\left(x-3\right)\left(x+5\right)$

$d)f\left(x\right)=2x^2+2x-4=\dots$

$\Delta =2^2-4\cdot 2\cdot \left(-4\right)=$

$=4+32=36$

$\sqrt{\Delta }=\sqrt{36}=6$

$x_1=\frac{-2-6}{2\cdot 2}=\frac{-8}{4}=-2$

$x_2=\frac{-2+6}{2\cdot 2}=\frac{4}{4}=1$

$\dots =2\left(x+2\right)\left(x-1\right)$

$e)f\left(x\right)=3x^2-10x+3=\dots$

$\Delta ={\left(-10\right)}^2-4\cdot 3\cdot 3=$

$=100-36=64$

$\sqrt{\Delta }=\sqrt{64}=8$

$x_1=\frac{10-8}{2\cdot 3}=\frac{2}{6}=\frac{1}{3}$

$x_2=\frac{10+8}{2\cdot 3}=\frac{18}{6}=3$

$\dots =3\left(x-\frac{1}{3}\right)\left(x-3\right)$

$f)f\left(x\right)=-2x^2+3x+2=\dots$

$\Delta =3^2-4\cdot \left(-2\right)\cdot 2=$

$=9+16=25$

$\sqrt{\Delta }=\sqrt{25}=5$

$x_1=\frac{-3-5}{2\cdot \left(-2\right)}=\frac{-8}{-4}=2$

$x_2=\frac{-3+5}{2\cdot \left(-2\right)}=\frac{2}{-4}=-\frac{1}{2}$

$\dots =-2x\left(x-2\right)\left(x+\frac{1}{2}\right)$