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factor completely 4x^2 - 24x - 8
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take 4 common
4(x^2-6x-2)
now use the formula of roots
x=\[\frac{ -b \pm \sqrt{b^2-4*a*c} }{ 2a }\]
ax^2+bx+c compare your equation with this and put value of a b c
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This is just simple factoring. I believe it may be prime, because I can only get as far as factoring out the 4. I end up with 4(x^2 - 6x - 8). I am unable to factor what's inside the parenthesis, so I am assuming the expression is Prime.
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