Respuesta:
Explicación paso a paso:
Ti¡o factorise the funtion [tex]f(x)=x^2 + 8x + 12[/tex] first we need to find where
f(x) =0, in other words, where [tex]x^2 + 8x + 12=0[/tex]
I'm going to use the metod of Po Shen Loh
[tex]x^2+ax+b=0\\(x+\alpha)(x+\beta)=0\\x^2+x(\alpha+\beta)+(\alpha\beta)=0\\\alpha=\frac{a}{2}+u\\\beta=\frac{a}{2}-u[/tex]
Now I'm going to change a by his value
[tex](\frac{8}{2}+u)(\frac{8}{2}-u)=12\\ (4+u)(4-u)=12\\ 16-u^2=12\\ u=\sqrt{16-12}\\ u=\sqrt{4}=2[/tex]
The factoring is:
[tex]\alpha=4+2=6\\\beta=4-2=2\\ (x+6)(x-2)=0[/tex]
