Question

what is the leading term of the polynomial f(x) defined below? f(x) = -7x² - 7 - 4x⁴

Explanation:

Step1: Recall the definition of leading term

The leading term of a polynomial is the term with the highest degree. The degree of a term \(ax^n\) is \(n\), where \(a\) is the coefficient and \(n\) is the exponent of \(x\).

Step2: Identify the degrees of each term

• For the term \(-7x^2\), the degree is \(2\) (since the exponent of \(x\) is \(2\)).
• For the term \(-7\) (which can be written as \(-7x^0\)), the degree is \(0\) (since the exponent of \(x\) is \(0\)).
• For the term \(-4x^4\), the degree is \(4\) (since the exponent of \(x\) is \(4\)).

Step3: Determine the term with the highest degree

Among the degrees \(2\), \(0\), and \(4\), the highest degree is \(4\). The term with degree \(4\) is \(-4x^4\).

Answer:

\(-4x^4\)