How many linear factors does a polynomial function f of degree n have, where n > 0?

Question

I don't know if it qualifys as calculus but im in a pre-calculus class

Answer 1

It has n factors, of course! A factor is a polynomial (for example, x - 7) which leaves remainder 0 when the function is divided by it. Put another, if a factor is set equal to 0, then x is a root (y-intercept). If (x + 4) is a factor of (x^3 - 16x), then the function touches the y-axis at x = -4. Think about a linear function (n = 1). It only touches/crosses the y-axis once. A parabola (n = 2) crosses twice. This excludes double, triple, etc. roots. When those exist, the function has less factors than n (although technically it still has many--they are just repeated!).