How do you factor completely: #3x^2- 21x + 30#?

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Answer 1 · 2015-07-24T13:38:02

#color(blue)((3x-6)(x-5) # is the factorised form.

#3x^2-21x+30#

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

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

#N_1*N_2 = a*c = 3*30 =90#
and
#N_1 +N_2 = b = -21#

After trying out a few numbers we get:
#N_1 = -15# and #N_2 =-6#
#(-15)*(-6) = 90#, and #-15+(-6)= -21#

#3x^2-21x+30 =3x^2-15x - 6x+30 #

#=3x(x-5) - 6(x-5) #

#(x-5)# is common to both terms
#color(blue)((3x-6)(x-5) # is the factorised form.