Final answer:
The leading term of a polynomial is the term with the highest degree. In this polynomial, x^5 has the highest degree of 5, making it the leading term, thus the correct option is a.
Explanation:
The leading term of a polynomial is the term with the highest degree. In this polynomial, x^5 has the highest degree of 5, making it the leading term.
A polynomial is an algebraic expression containing two or more terms. The terms can be variables, constants, and coefficients. The leading term of a polynomial is the term with the highest degree. In this case, the highest degree is 5, which belongs to the term x^5. Therefore, x^5 is the leading term of the given polynomial.
To further understand why x^5 is the leading term, let's break down the given polynomial into its individual terms:
x^5 + 5x^2y^4 + xy + 8x - 9
The term x^5 has a coefficient of 1, which means it is multiplied by 1. The degree of x^5 is 5, which means it is raised to the fifth power. When we compare it to the other terms, we can see that it has the highest degree. Therefore, it is the leading term.
Moreover, the other terms in the polynomial have lower degrees, making them lower in terms of importance. For example, 5x^2y^4 has a degree of 6, xy has a degree of 2, 8x has a degree of 1, and -9 has a degree of 0. Since x^5 has a higher degree than all of these terms, it is considered the leading term.
In conclusion, the leading term of the polynomial x^5 + 5x^2y^4 + xy + 8x - 9 is x^5. This is because it has the highest degree of 5, making it the most significant term in the expression. Understanding the concept of leading terms is crucial in simplifying and solving polynomials, as it helps us identify the most significant term and its corresponding degree, thus the correct option is a.