Based on the degree, what is the greatest number of zeros the polynomial f(x)=5x4+3x2
could have?(1 point)
The degree of a polynomial is determined by the highest power of x in the polynomial. In this case, the highest power of x is 4. Therefore, the degree of the polynomial is 4.
Since the polynomial does not have any terms with x^3, x^2, x^1, or x^0, it means that there are no zeros in the polynomial. Therefore, the greatest number of zeros the polynomial f(x)=5x^4+3x^2 could have is zero.
To determine the greatest number of zeros a polynomial can have based on its degree, we need to consider the highest exponent in the polynomial.
In the given polynomial f(x) = 5x^4 + 3x^2, the highest exponent is 4. So, the degree of this polynomial is 4.
According to the fundamental theorem of algebra, a polynomial of degree n can have at most n distinct zeros. Therefore, the greatest number of zeros the polynomial f(x) = 5x^4 + 3x^2 could have is 4.