Answer :
To determine the greatest number of zeros a polynomial could have, we need to look at its degree. The degree of the polynomial is the highest power of [tex]\( x \)[/tex] in the expression.
For the polynomial [tex]\( f(x) = 7x^6 - 5x^5 + x \)[/tex], the degree is 6 because the highest power of [tex]\( x \)[/tex] in the polynomial is [tex]\( x^6 \)[/tex].
According to the Fundamental Theorem of Algebra, a polynomial of degree [tex]\( n \)[/tex] can have at most [tex]\( n \)[/tex] zeros. This includes real and complex zeros, and some of them might be repeated (also known as having multiplicity).
Since the degree of the polynomial [tex]\( f(x) \)[/tex] is 6, the greatest number of zeros it could have is 6.
So, the greatest number of zeros that the polynomial [tex]\( f(x) = 7x^6 - 5x^5 + x \)[/tex] could have is 6.
For the polynomial [tex]\( f(x) = 7x^6 - 5x^5 + x \)[/tex], the degree is 6 because the highest power of [tex]\( x \)[/tex] in the polynomial is [tex]\( x^6 \)[/tex].
According to the Fundamental Theorem of Algebra, a polynomial of degree [tex]\( n \)[/tex] can have at most [tex]\( n \)[/tex] zeros. This includes real and complex zeros, and some of them might be repeated (also known as having multiplicity).
Since the degree of the polynomial [tex]\( f(x) \)[/tex] is 6, the greatest number of zeros it could have is 6.
So, the greatest number of zeros that the polynomial [tex]\( f(x) = 7x^6 - 5x^5 + x \)[/tex] could have is 6.
