Question

How to factor 2n^2+3n-9 without splitting the middle term

Answer 1

$2n^2+3n-9= \\\\ a=2 \\ b=3 \\ c=-9 \\\\ \Delta= 3^2-4*2*(-9)=9+72\to\boxed{81} \\\\ x_1;x_2=\frac{-3 +\-\sqrt{81}}{2*2}= \frac{-3+/- 9}{4} \\\\ x_1=\frac{-3+9}{4}=\frac{6}{4}\to\boxed{\frac{3}{2}} \\\\ x_2=\frac{-3-9}{4}=\frac{-12}{4}\to\boxed{-4} \\\\ 2n^2+3n-9=(x-\frac{3}{2})(\x+4)$