Can #y= 3x^2-30x-72 # be factored? If so what are the factors ?

1 Answer
Alan N.
Apr 29, 2016

Yes.
Factors are: #3, (x-12), (x+2)#

Explanation:

#y = 3x^2-30x-72#
By inspection, 3 is a factor #-> y=3(x^2-10x-24)#

Since the constant term is #-24# and the coefficient of #x# is #-10#, we now look for factors of #24# which differ by #10#

These are 12 and 2.

Since the constant term is #-ve# the constants in the factors must have different sign. Also, since the coefficient of #x# is also #-ve# the larger factor of #24# must be #-ve#.

Hence the second and third factors are #(x-12) and (x+2)#

Therefore: #y =3(x-12)(x+2)#

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