Are polynomials with 5 terms never factorable?

Answer 1

The short answer is "No."

The Fundamental Theorem of the Algebra states that every single variable polynomial has at least one complex zero. A zero means that the polynomial has a facto. Therefore all polynomials are factorable.

Answer 2

Here's a 5 term polynomial

x^8 + x^7 + x^6 + x^5 + x^4

factors of

(x^4)(x^4 + x^3 + x^2 + x + 1) or

(x)(x)(x)(x)(x^4+x^3+x^2+1), five factors of a 5 term polynomial with real factors, no imaginary factors needed