Question

Factor the Expression. If the expression cannot be factored, say so. 8.) x^2 - 4x - 12

Answer 1

To factor an expression of the form:

$x^2+bx+c$

we find two numbers B and C that fulfills the following properties:

$\begin{gathered} B+C=b \\ BC=c \end{gathered}$

In this case we have b=-4 and c=-12. We can choose B=-6 and C=2. Then we write the expression as:

$x^2-4x-12=x^2-6x+2x-12$

and we factor the common factors in the first two and last terms:

$\begin{gathered} x^2-4x-12=x^2-6x+2x-12 \\ =x(x-6)+2(x-6) \\ =(x+2)(x-6) \end{gathered}$

Therefore:

$x^2-4x-12=(x+2)(x-6)$