According to the Fundamental Theorem of Algebra, what is the greatest number of zeros the polynomial f(x)=7x6−5x5+x (1 point) Responses 7 7 6 6 5 5 11

Answer 1

According to the Fundamental Theorem of Algebra, a polynomial of degree \( n \) can have at most \( n \) roots (or zeros), counting multiplicities.

The polynomial given is \( f(x) = 7x^6 - 5x^5 + x \). The highest degree of this polynomial is 6 (from the term \( 7x^6 \)).

Therefore, the greatest number of zeros that this polynomial can have is:

6

So the correct response is 6.