Is it possible to factor #y=6x^2+48x-54#? If so, what are the factors?

1 Answer
Dec 15, 2015

Answer:

Yes; #x=9 and x=-1#

Explanation:

Factoring #Ax^2+Bx+C#
Find factors of #AC# that add up to #B#

Original equation:
#y=6x^2+48x-54#

Simplify by factoring out #6#:
#y=6(x^2+8-9)

Multiply #A# by #C#:
#1•(-9)#
#-9#
x
Find factors of #-9#
#1, -9#
#9,-1#
#3,-3#

Determine which of the factors add up to #B.# Here, #B=8#.

The two factors that add up to #8# are #9,-1#.

Now, you can plug the factors back into the equation.
#y=6(x+9)(x-1)#

Or you can set the factors equal to zero and solve for #x#
You should end up with #x=1# and #x=-9#.