How do you factor 6x2−6x−11x+11?

1 Answer
George C.
Apr 26, 2016

6x2−6x−11x+11=(6x−11)(x−1)

Explanation:

Factor by grouping:

6x2−6x−11x+11

=(6x2−6x)−(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:

6x2−17x+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.

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