SOLUTION: Factor: a^2-6a-27 How do I do this ? Thanks for your help and time !

Question 27735: Factor:
a^2-6a-27
How do I do this ?
Thanks for your help and time !
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
a^2-6a-27 (this is a quadratic expression in a)
= a^2+(-9a+3a)-27
[Observe that the product of the coeff of a^2 and the constant term is
(1)X(-27) = -27 = -(1x3x3x3)
and therefore we group the numerical factors 1,3,3,3 without leaving any factor into two sets in such a way that as the product is negative and the mid term also negative, the two sets should be of oppostite sign with the larger numerical set having the sign of the mid term.That is our sets
are -(1x3x3) and (3)giving -6 = (-9+3) so that -6a = -9a+3a and
(-9a)X(3a) = -27a^2][The golden rule is: split the middle term into two parts whose product is the product of the first and the last term]
=a^2-9a+3a-27
= (a^2-9a)+(3a-27)
=a(a-9) + 3(a-9)
=ap +3p where p = (a-9)
=p(a+3)
=(a-9)(a+3)
Note: Please refer to my examples, explanations and illustrations
given under the answer for the problem 27662
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