Let's simplify the polynomial [tex]\(5 s^6 t^2 + 6 s t^9 - 8 s^6 t^2 - 6 t^7\)[/tex] and analyze its terms.
Step-by-Step Simplification:
1. Combine like terms.
- The terms [tex]\(5 s^6 t^2\)[/tex] and [tex]\(-8 s^6 t^2\)[/tex] are like terms because they share the same variables and degrees.
- The simplification of these terms is:
[tex]\[
5 s^6 t^2 - 8 s^6 t^2 = (5 - 8) s^6 t^2 = -3 s^6 t^2
\][/tex]
2. Collect the simplified terms:
- [tex]\(-3 s^6 t^2\)[/tex]
- [tex]\(6 s t^9\)[/tex]
- [tex]\(-6 t^7\)[/tex]
So the simplified polynomial is:
[tex]\[
-3 s^6 t^2 + 6 s t^9 - 6 t^7
\][/tex]
Determine the Number of Terms:
- The polynomial now consists of three distinct terms: [tex]\(-3 s^6 t^2\)[/tex], [tex]\(6 s t^9\)[/tex], and [tex]\(-6 t^7\)[/tex].
Determine the Degree of the Polynomial:
- The degree of a term in a polynomial is the sum of the exponents of the variables in that term.
1. For [tex]\(-3 s^6 t^2\)[/tex], the degree is [tex]\(6 + 2 = 8\)[/tex].
2. For [tex]\(6 s t^9\)[/tex], the degree is [tex]\(1 + 9 = 10\)[/tex].
3. For [tex]\(-6 t^7\)[/tex], the degree is [tex]\(7\)[/tex].
- The degree of the polynomial is determined by the term with the highest degree, which is [tex]\(6 s t^9\)[/tex] with a degree of [tex]\(10\)[/tex].
Conclusion:
The simplified polynomial has 3 terms and a degree of 10.
Therefore, the correct statement is:
- It has 3 terms and a degree of 10.
