\({-x^2 - 14x -24}\)

it's two numbers that multiply to ac and add to b right? so that makes -24 positive... which isn't factorable? so would i use the quadratic formula?

Guest Jun 5, 2018

This is factorable:


\(-x^2-14x-24=0\\ =(−x−2)(x+12)=0\\ x_1=-2;x_2=-12\)


I'm assuming that there is a equal zero at the end of the equation. 


I hope this helped,


GYanggg  Jun 5, 2018

....or maybe you can see it more clearly this way:


Multiply both sides of the equation by  -1  to get


x^2+14x+24 = 0


Now factor


(x+2)(x+12) = 0      x = -2 or -12

ElectricPavlov  Jun 5, 2018

I am not sure why the answerers have treated an expression as an equation. 


Anyway, as the other answerers have pointed out, the trinomial \(-x^2-14x-24\) is factorable. When factoring, I have one suggestion: Manipulate the expression so that the quadratic term (the x^2-term) is positive. 


\(-x^2-14x-24\) Factor out a negative one so that the quadratic term is positive.
\(-(\textcolor{red}{x^2+14x+24})\) Now, factor the quadratic highlighted in red. Using the "AC" method, ac=24 and b=14. 12 and 2 are the only pair of numbers that multiply to obtain 24 and add to obtain 14.
\(-(x+12)(x+2)\) There you go! You have factored this polynomial. 
TheXSquaredFactor  Jun 5, 2018

Good point x^2    I was working off of yangg's example and not the question.   my mistake....BUT since the questioner asked about the quadratic formula, I guess we can assume   = 0  

ElectricPavlov  Jun 5, 2018
edited by ElectricPavlov  Jun 5, 2018

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