Question

Factor X squared plus 2X -24

Answer 1

The factors of a quadratic polynomial are:

`(x-x_1)and(x-x_2)`

where x1 and x2 are the roots (or zeros) of the polynomial

`x^2+2x-24`

Using the quadratic formula, we get:

`\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=(-2+10)/(2)=4 \\ x_2=(-2-10)/(2)=-6 \end{gathered}`

Then, the factor are: (x - 4) and (x + 6)