Question

1. $f(x)=x^{5}-5x^{4}+2x^{3}-10x^{2}-48x + 240$

a) 5 b) 6
c) 7 d) 6, 4, 2, or 0
how many total roots/zeros are there in the polynomial.

Explanation:

Step1: Identify polynomial degree

The polynomial is $f(x)=x^5 - 5x^4 + 2x^3 - 10x^2 - 48x + 240$, degree $n=5$.

Step2: Apply Fundamental Theorem of Algebra

A degree-$n$ polynomial has exactly $n$ total roots (counting complex roots and multiplicities). So total roots = $5$.

Answer:

A) 5