Given the two expressions below: 1) 4x2 − 8x + 9 2) 3x2 + 2y + 6 is the sum of the two expressions above a polynomial? why or why not?

Sum of polynomials are always polynomials.

Note that despite it's name, single constants, monomials, binomials, trinomials, and expressions with more than three terms are all polynomials.
For example,
0, π sqrt(2)x, 4x+2, x^2+3x+4, x^2-x^2, x^5+x/ π -1
are all polynomials.

What makes an expression NOT a polynomial?
Expressions that contain non-integer or negative powers of variables, rational functions, infinite series.
For example,
sqrt(x+1), 1/x+4, 1+x+ x^2/2!+x^3/3!+x^4/4!+, (5x+3)/(6x+7)
are NOT polynomials.