How do you factor #6x^2 - 6x - 11x + 11#?

1 Answer
Apr 26, 2016

Answer:

#6x^2-6x-11x+11=(6x-11)(x-1)#

Explanation:

Factor by grouping:

#6x^2-6x-11x+11#

#=(6x^2-6x)-(11x-11)#

#=6x(x-1)-11(x-1)#

#=(6x-11)(x-1)#

Note that the hard/fun part has been done for you already in the question - the splitting of the middle term into #-6x-11x#.

Commonly this would not be done for you: The problem would be given in the form:

#6x^2-17x+11#

and it would be up to you to find the split.

In this particular case there is a shortcut: Notice that the sum of the coefficients is #0#. That is: #6-17+11 = 0#. When the sum of the coefficients is #0#, then #x=1# is a zero and #(x-1)# is a factor.