I need help with this Polynomial

Question

Find all zeros of the function algebraically. Show the factorization of the polynomial. State the multiplicity of each solution f(x)= x^5 +4x^4+10x^3+22x^2+25x+10

Answer 1

Hi Tolani! Here's some advice to help you get started.

First off, the degree of this polynomial is 5 so we know there will be up to 5 real factors. Some of these factors could repeat. To figure out what factors to try, we'll first look at our constant term (10). The factors of 10 are +/-1, +/-2, +/-5, and +/-10. This means that some factors you could try dividing x^5 +4x^4+10x^3+22x^2+25x+10 by are (x+1), (x-1), (x+2), (x-2), (x+5), (x-5), (x+10), and (x-10).

Let me know if you're not sure how to divide polynomials either using synthetic division or long division.