Question

find the degree, leading coefficients, and the maximum number of real zeros of the polynomial. $f(x)=4x^{6}+x^{7}-2x^{4}-5$. degree = . leading coefficient = . maximum number of real zeros =

Explanation:

Step1: Identify degree of polynomial

The degree of a polynomial is the highest power of the variable. For \(f(x)=4x^{6}+x^{7}-2x^{4}-5\), the highest - power of \(x\) is 7. So the degree is 7.

Step2: Identify leading coefficient

The leading coefficient is the coefficient of the term with the highest degree. The term with the highest degree is \(x^{7}\) and its coefficient is 1.

Step3: Determine maximum number of real zeros

The maximum number of real zeros of a polynomial is equal to its degree. Since the degree is 7, the maximum number of real zeros is 7.

Answer:

Degree: 7
Leading Coefficient: 1
Maximum number of real zeros: 7