Question

the leading coefficient of the polynomial $4x^{4} + 0x^{3} + 0x^{5} + 5x + 7$ is ----
select the correct response:
3
7
4
5
0

Explanation:

Step1: Recall leading term definition

The leading term of a polynomial is the term with the highest degree. First, we need to find the degree of each term in the polynomial \(4x^{4}+0x^{3}+0x^{5}+5x + 7\). The degree of a term \(ax^{n}\) is \(n\). So:

• For \(4x^{4}\), degree is \(4\).
• For \(0x^{3}\), degree is \(3\).
• For \(0x^{5}\), degree is \(5\) (but coefficient is \(0\)).
• For \(5x\), degree is \(1\).
• For \(7\), degree is \(0\) (constant term).

Step2: Identify the leading term

We compare the degrees. The term \(0x^{5}\) has degree \(5\), but its coefficient is \(0\), so it doesn't contribute. The next highest degree is \(4\) from the term \(4x^{4}\).

Step3: Find the leading coefficient

The leading coefficient is the coefficient of the leading term. The leading term here is \(4x^{4}\), so its coefficient (the leading coefficient) is \(4\).

Answer:

4