Factor $x^2+10x+15$?

Question

How can you factor $x^2+10x+15$? The form $Ax^2+Bx+C$, where $B$ is the sum of $2$ factors of $C$ (and $\lvert A\rvert=1$) does not work.

Answer 1

$$ x^2+10x+15=(x^2+10x+25)-10=(x+5)^2-(\sqrt{10})^2. $$ Now use, $a^2-b^2=(a-b)(a+b)$.

Answer 2

Use the quadratic formula:

$$ x_1,_2 = \frac{ - b \pm \sqrt {b^2 - 4ac} }{2a} \text{ when } ax^2 + bx + c = 0 $$

$a=1$, $b=10$, $c=15$,

This will get you 2 roots. You could then write your function as:

$(x-x_1)(x-x_2)$