factor the polynomial

17xy{4} + 51x{2}y{3}

To factor the polynomial 17xy^4 + 51x^2y^3, we can factor out the greatest common factor of the terms, which in this case is 17xy^3. This gives us:

17xy^3 (y + 3x)

So, the factored form of the polynomial 17xy^4 + 51x^2y^3 is 17xy^3 (y + 3x).