How do you factor the trinomial #16x^4y^3 − 20x^2y^5 + 8xy^7#?

1 Answer
Feb 10, 2016

#16x^4y^3-20x^2y^5+8xy^7=4xy^3(4x^3-5xy^2+2y^4)#

Explanation:

First notice that all of the individual terms are divisible by #4xy^3#, so separate that out as a factor:

#16x^4y^3-20x^2y^5+8xy^7=4xy^3(4x^3-5xy^2+2y^4)#

The other factor is non-homogeneous: #4x^3# and #5xy^2# are of degree #3# and #2y^4# is of degree #4#. So it has no simpler homogeneous factors. Neither are its degrees in any kind of arithmetic sequence. This all points towards it not being reducible to a product of simpler factors.