How do you factor #x^2+11x-27#?

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Answer 1 · 2015-06-17T21:39:24

The factors can be derived from the quadratic formula as:

#x^2+11x-27 = (x+(11+sqrt(229))/2)(x+(11-sqrt(229))/2)#

#x^2+11x-27#

is of the form #ax^2+bx+c# with #a=1#, #b=11# and #c=-27#.

This has discriminant #Delta# given by the formula:

#Delta = b^2-4ac = 11^2-(4xx1xx-27)#

#=121+108 = 229#

Since this is positive but not a perfect square, the quadratic has irrational factors, which we can derive from the quadratic formula:

#x^2+11x-27 = 0# has roots given by the formula:

#x = (-b +- sqrt(Delta))/(2a) = (-11+-sqrt(229))/2#

Hence

#x^2+11x-27 = (x+(11+sqrt(229))/2)(x+(11-sqrt(229))/2)#