Which of the following statements are correct about the algebraic expression 2y^2+17x^2+14x^2y+8xy^2+1?

The assertion that the coefficients of the expression (2y^2 + 17x^2 + 14x^2y + 8xy^2 + 1) are 2, 17, 14, 8, and 1 is correct because coefficients are the numerical factors that multiply each term of the polynomial. In this case, the coefficients correspond to the numbers in front of each term:

• The coefficient of (y^2) is 2.

• The coefficient of (x^2) is 17.

• The coefficient of (x^2y) is 14.

• The coefficient of (xy^2) is 8.

• The constant term, which can be viewed as (0x) or (0y), has a coefficient of 1.

This captures all the numerical values associated with the variable terms and the constant in the expression, confirming these are the correct coefficients.

The other statements regarding variables, like terms, and the degree of the expression require further analysis. Although some of these may hold some validity, they do not have the same definitive correctness as the identification of the coefficients in this context.