Question

How would you factor this

0= x^2+x-2

Answer 1

\[(x+2)(x-1)\]

Answer 2

\[ax^2+bx+c=0\]\[x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]\[(x-x_1)(x-x_2)=0\]
_____
\[x^2+x-2=0\]\[x_{1,2}=\frac{-1\pm\sqrt{1^2-4\times 1\times -2}}{2\times1}\\
\qquad=\frac{-1\pm\sqrt{1+8}}{2}\\
\qquad=\frac{-1\pm\sqrt 9}{2}\\
\qquad=\frac{-1\pm3}{2}\\
\qquad=-\frac42,\frac{2}2\\
\qquad=-2,1\]
\[(x+2)(x-1)=0\]