How do you factor #5y^{2}+12y-32#?

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Answer 1 · 2016-10-21T20:56:26

The factorised form is #(5y-8)(y+4)#
or #5(y+4)(y-8/5)#

You can use the following
#(1)#
#5y^2+12y-32=5y^2+20y-8y-32 #
#= 5y(y+4)-8(y+4)#
#y+4# is a common factor
#=(y+4)(5y-8)#

#(2)#
By completing the squares and factorising
#5y^2+12y-32=5(y^2+(12/5)y-32/5)#

#=5(y^2+(12/5)y+36/25-32/5-36/25)#

#=5((y+6/5)^2 -196/25)#

#=5((y+6/5)^2-(14/5)^2)#

#=5((y+6/5+14/5)(y+6/5-14/5))#

#=5(y+20/5)(y-8/5)#