How do you factor the trinomial #x^2-xy-12y^2#?

1 Answer
George C.
Jan 2, 2016

Split #12# into two factors that differ by #1# to find:

#x^2-xy-12y^2 = (x-4y)(x+3y)#

Explanation:

Because this is a homogeneous polynomial of degree #2#,
this is essentially the same problem as factoring #t^2-t-12#

Split #12# into two factors which differ by #1#. The pair #4, 3# works.

Hence:

#x^2-xy-12y^2 = (x-4y)(x+3y)#

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