Yes, you can say "a polynomial with a degree of 3," but it is more customary and precise to say "a polynomial of degree 3." Both phrases convey the same meaning, but "of degree 3" is the standard terminology in mathematics.
You are correct that a polynomial of degree 3 can have up to 3 zeros (real or complex) and can generally be factored into the product of linear expressions (for example, \( a(x - r_1)(x - r_2)(x - r_3) \), where \( r_1, r_2, r_3 \) are the roots, and \( a \) is a leading coefficient). If the polynomial has less than 3 distinct roots, some of the linear factors may repeat, reflecting the multiplicity of the roots.