# Question #15ac4

Jan 29, 2015

In the Real Field it is not possible.
If you want, but I don't think it is your case, could be factorized in the Complex Field.

A polinomial of 2° degree could be factorize only if the associate equation of 2°degree (i.e. $2 {x}^{2} + 8 x + 9 = 0$) has the $\Delta$ positive or zero.

I remember that the equation of 2° degree could be written:

$a {x}^{2} + b x + c = 0$ and the $\Delta$ is $\Delta = {b}^{2} - 4 a c$.

So:

if $\Delta = 0$ than the polynomial is a binomial square, it is sufficient to find the double solution of the equation, ${x}_{1}$, and then:

$a {x}^{2} + b x + c = a {\left(x - {x}_{1}\right)}^{2}$.

if $\Delta = 0$ than the polynomial could be factorized if the two solutions, ${x}_{1} , {x}_{2}$, are found, and then:

$a {x}^{2} + b x + c = a \left(x - {x}_{1}\right) \left(x - {x}_{2}\right)$, don't forget the $a$.