Certainly! Let's analyze the given expression step-by-step to determine the number of terms in it.
The expression given is:
[tex]\[
6x^2 - \frac{x}{3} - 2x^3 + 15 - x^5 + 4x^4
\][/tex]
1. Identify each term:
- The first term is [tex]\(6x^2\)[/tex].
- The second term is [tex]\(-\frac{x}{3}\)[/tex]. This can also be written as [tex]\(-\frac{1}{3}x\)[/tex], but it remains a single term in the expression.
- The third term is [tex]\(-2x^3\)[/tex].
- The fourth term is [tex]\(15\)[/tex].
- The fifth term is [tex]\(-x^5\)[/tex].
- The sixth term is [tex]\(4x^4\)[/tex].
2. Count the number of terms:
- [tex]\(6x^2\)[/tex] is 1 term.
- [tex]\(-\frac{x}{3}\)[/tex] is 1 term.
- [tex]\(-2x^3\)[/tex] is 1 term.
- [tex]\(15\)[/tex] is 1 term.
- [tex]\(-x^5\)[/tex] is 1 term.
- [tex]\(4x^4\)[/tex] is 1 term.
By counting each of these terms, we see there are a total of six distinct terms in this polynomial expression.
Thus, the number of terms in the expression [tex]\(6x^2 - \frac{x}{3} - 2x^3 + 15 - x^5 + 4x^4\)[/tex] is:
[tex]\[
\boxed{6}
\][/tex]
