How do you factor completely #x^2 - 3x - 24#?

1 Answer
George C.
Nov 19, 2015

Use the quadratic formula to find:

#x^2-3x-24 = (x-(3+sqrt(105))/2)(x-(3-sqrt(105))/2)#

Explanation:

#x^2-3x-24# is in the form #ax^2+bx+c# with #a=1#, #b=-3# and #c=-3# and has zeros given by the quadratic formula:

#x = (-b+-sqrt(b^2-4ac))/(2a)#

#=(3+-sqrt((-3)^2-(4xx1xx(-24))))/(2xx1)#

#=(3+-sqrt(9+96))/2#

#=(3+-sqrt(105))/2#

Hence:

#x^2-3x-24 = (x-(3+sqrt(105))/2)(x-(3-sqrt(105))/2)#

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