If x1 and x2 are solutions of a quadratic equation, the quadratic trinomial can be expressed as the product of linear factors:
\begin{align} ax^{2}+bx+c&=a(x-x_{1})(x-x_{2})\\ \end{align}
where,
x1, x2— roots of the quadratic trinomial.
If c=0:
\begin{align} ax^{2}+bx&=x(ax+b)\\ \end{align}
When the quadratic equation is factored, the equation takes the following form:
$$x^{2}+px+q=(x-x_{1})(x-x_{2})$$
The equations also hold when x1 = x2.