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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 -.

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

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