Question

Find all roots of the polynomial function F(x)=x^2-2x-24

Answer 1

$f(x)=x^2-2x-24\\\\ x^2-2x-24=0\\\\ Factorization:\\ x^2+4x-6x-24=0\\\\ x(x-6)+4(x-6)=0\\\\(x+4)(x-6)=0\\\\ x=-4\ \ or \ \ x=6$

Answer 2

$f(x)=x^2-2x-24=x^2+4x-6x-24=x(x+4)-6(x+4)=\\\\=(x+4)(x-6)\\\\f(x)=0\ \ \ \Leftrightarrow\ \ \ (x+4)(x-6)=0\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \Leftrightarrow\ \ \ x+4=0\ \ \ \ \ or\ \ \ \ \ x-6=0\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \Leftrightarrow\ \ \ x=-4\ \ \ \ \ \ \ \ or\ \ \ \ \ x=6$