The factors of a quadratic polynomial are:
[tex](x-x_1)and(x-x_2)[/tex]where x1 and x2 are the roots (or zeros) of the polynomial
[tex]x^2+2x-24[/tex]Using the quadratic formula, we get:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-2\pm\sqrt[]{2^2-4\cdot1\cdot(-24)}}{2\cdot1} \\ x_{1,2}=\frac{-2\pm\sqrt[]{100}}{2} \\ x_1=\frac{-2+10}{2}=4 \\ x_2=\frac{-2-10}{2}=-6 \end{gathered}[/tex]Then, the factor are: (x - 4) and (x + 6)