# why do we factor the roots of an equation as $x-x_1$ and not $x+x_2$

why do we factor the roots of an equation as $$x-x_1$$ and not $$x+x_2$$. In the quadratic formula b= the sum of the roots multiplied by the leading coefficient and -.

• If $x_1$ is a root, then $x-x_1$ is a factor, but in general not $x+x_1$ (unless $x_1=0$) – Peter Mar 16 at 14:54
• let $x = x_1$ then subtract both sides by $x_1$ you get $(x-x_1) = 0$ – user29418 Mar 16 at 14:56

If you factor a polynomial then the product is $$\ 0\$$ if and only if one of the factors is $$\ 0\$$. Hence, the solution $$\ x_1\$$ corresponds to the factor $$\ x-x_1\$$ which is $$\ 0\$$ for $$\ x=x_1\$$.