Is $2x^3-4x^5+3$2x3−4x5+3 a polynomial?

Yes, it is a polynomial.

No, it is not a polynomial.

Is $3x^3+\frac{2}{x^7}-1$3x3+2x7−1 a polynomial?

Is $\sqrt{2}x^6+7x$√2x6+7x a polynomial?

For the polynomial $P\left(x\right)=2x^7+2x^5+2$P(x)=2x7+2x5+2

Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.