Question

Consider the degree 5 polynomial function P(x)=x^5-4x^3+2x^2+3x-5. You do not need to factor this polynomial to answer the question. How many linear factors is P guaranteed to have? Explain.

Answer 1

5.

Explanation:

According to the Linear Factorization Theorem, a polynomial function will have the same number of factors as its degree. We also know that these factors will have the form (x - c) where c is a complex number.

In this problem, and without factoring the polynomial, we observe that the polynomial function is a 5 degree function so we can know that it will have 5 linear factors.