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

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Answer 1 · 2015-06-03T08:43:32

#y^2 - 2y - 3 #

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 = 1*-3 = -3#
and
#N_1 +N_2 = b = -2#

After trying out a few numbers we get #N_1 = -3# and #N_2 =1#
#-3*1 = -3#, and #1+(-3)= -2#

#y^2 - 2y - 3 = y^2 - 3y + y- 3 #

# y^2 - 3y + y- 3 = y(y-3) + 1(y- 3) #

#(y-3)# is a common factor to each of the terms

#=color(green)((y+1)(y-3)#