How do you factor #5y^2-3y-2#?

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Answer 1 · 2015-08-10T15:23:49

#= color(blue)((5y+2)(y-1) #

#5y^2−3y-2#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ay^2 + by + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 5*-2 = -10#
and,
#N_1 +N_2 = b = -3#

After trying out a few numbers we get #N_1 = -5# and #N_2 =2#
#-5*2 = -10#, and #2+(-5)=-3#

#5y^2−color(blue)(3y)-2 = 5y^2−color(blue)(5y+2y)-2#

#= 5y(y-1) +2(y-1)#

#= color(blue)((5y+2)(y-1) #