Question

1. solve by factoring ( m^2 + 2m - 24 = 0 )

□ =0 (factored form)
( m = )□, ( m = )□ (list from least to greatest)
show your work

1. find the roots of the equation found below by using quadratic formula ( x = \frac{-b pm sqrt{b^2 - 4ac}}{2a} )

( x^2 - 4x + 1 = 0 )
( x = )□

Explanation:

Step1: Factor the quadratic

Find two numbers: product=-24, sum=2 → 6 and -4
$(m + 6)(m - 4) = 0$

Step2: Solve for m

Set each factor to 0:
$m + 6 = 0 \Rightarrow m = -6$
$m - 4 = 0 \Rightarrow m = 4$

Step3: Identify quadratic coefficients

For $x^2 - 4x + 1 = 0$, $a=1$, $b=-4$, $c=1$

Step4: Apply quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{4 \pm \sqrt{16 - 4}}{2} = \frac{4 \pm \sqrt{12}}{2} = \frac{4 \pm 2\sqrt{3}}{2} = 2 \pm \sqrt{3}$

Answer:

Factored form: $(m + 6)(m - 4)$
$m = -6$, $m = 4$
$x = 2 + \sqrt{3}$, $x = 2 - \sqrt{3}$