Check whether the following algebraic expression is a polynomial in a literal?

$1+2x+3x^2+4x^3$

Check whether the following algebraic expression is a polynomial in a literal?

$5x^2-7x+\frac{3}{x }$

Check whether the following algebraic expression is a polynomial in a literal?

$7-y^2$

Check whether the following algebraic expression is a polynomial in a literal?

$\frac{1}{x}+x$

Check whether the following algebraic expression is a polynomial in a literal?

$\frac{1}{8}x+\frac{1}{9}$

Check whether the following algebraic expression is a polynomial in a literal.

$1+a^4$

Write the degree of the polynomial $x+2$

Write the degree of the polynomial $2x-3$

Write the degree of the polynomial $7-{\mathrm{y}}^2$