Question

1. $f(x)=x^{8}-5x^{4}+4$

a) 3 or 1
b) 7, 5, 3, or 1
c) 10
d) 8
q use the fundamental theorem of algebra to state the number of zeros/solutions/roots of the polynomial.

Explanation:

Step1: Recall Fundamental Theorem of Algebra

A polynomial of degree $n$ has exactly $n$ complex roots (counting multiplicities).

Step2: Identify polynomial degree

For $f(x)=x^8 - 5x^4 + 4$, the highest power of $x$ is 8, so degree $n=8$.

Step3: Apply theorem to find roots

By the theorem, the number of zeros is equal to the degree.

Answer:

D) 8