1. ## Factoring

Hello

I am having some difficulty factoring the following problem. I would appreciate some help. This is what I have come up with thus far. See attachment

2. The question asks you to factor, while the quadratic formula just solves for x.

$\displaystyle x^2+23x+24$

however you can't factor $\displaystyle x^2+23x+24$

but, you can factor $\displaystyle x^2+23x+42$ into $\displaystyle (x+21)(x+2)$ (maybe you just had a typo)

also this isn't an equation, it's an expression, but if you set $\displaystyle x^2+23x+24$ equal to something, it becomes easy to factor.

3. Hello, pashah!

What you have written is correct ... so far.

Factor the following equation. . . . not an equation

$\displaystyle b)\;\;x^2 + 23x + 24$

Use the quadratic formula to factor.
The solutions to the quadratic, when set equal to zero, are:

$\displaystyle x \:=\:\frac {-b \pm \sqrt{b^2 - 4ac}}{2a}$

$\displaystyle \frac{-(23) + \sqrt{(23)(23) - 4(1)(24)}}{2(1)}$

$\displaystyle \frac{-(23) - \sqrt{(23)(23) - 4(1)(24)}}{2(1)}$

How about doing the arithmetic? . $\displaystyle x \;= \;\frac{-23 \pm\sqrt{433}}{2}$

Then write the factors? . $\displaystyle \left(x - \frac{-23 + \sqrt{433}}{2}\right)\,\left(x - \frac{-23 - \sqrt{433}}{2}\right)$