Question

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?

Answer 1

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.