How do you factor #5p^2 - p - 6 #?

1 Answer
Don't Memorise
May 30, 2015

#5p^2 - p - 6 #

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like #ap^2 + bp + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 5*(-6) = -30#
and
#N_1 +N_2 = b = -1#

After trying out a few numbers we get #N_1 = -6# and #N_2 =5#
#-6*(5) = -30#, and #5+(-6)= -1#

#5p^2 - p - 6 = 5p^2 +5p -6p- 6#

#= 5p(p+1)-6(p+1)#

# =color(blue)((5p - 6)(p+1)#

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