Question

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

Answer 1

`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.