Let's simplify the polynomial and analyze its terms step by step to determine both the number of terms and the degree of the polynomial.
Given polynomial:
[tex]\[5 s^6 t^2 + 6 s t^9 - 8 s^6 t^2 - 6 t^7\][/tex]
### Step 1: Combine like terms
First, we notice that there are like terms in the polynomial that we need to combine:
- The terms [tex]\(5 s^6 t^2\)[/tex] and [tex]\(-8 s^6 t^2\)[/tex] are like terms.
Combine these terms:
[tex]\[5 s^6 t^2 - 8 s^6 t^2 = (5 - 8) s^6 t^2 = -3 s^6 t^2\][/tex]
Now the polynomial becomes:
[tex]\[-3 s^6 t^2 + 6 s t^9 - 6 t^7\][/tex]
### Step 2: Count the number of terms
After combining like terms, the simplified polynomial is:
[tex]\[-3 s^6 t^2 + 6 s t^9 - 6 t^7\][/tex]
This polynomial now has 3 distinct terms:
1. [tex]\(-3 s^6 t^2\)[/tex]
2. [tex]\(6 s t^9\)[/tex]
3. [tex]\(-6 t^7\)[/tex]
### Step 3: Determine the degree of the polynomial
To find the degree of the polynomial, we identify the degree of each term. The degree of a term is the sum of the exponents of the variables in that term.
- The degree of [tex]\(-3 s^6 t^2\)[/tex] is [tex]\(6 + 2 = 8\)[/tex].
- The degree of [tex]\(6 s t^9\)[/tex] is [tex]\(1 + 9 = 10\)[/tex].
- The degree of [tex]\(-6 t^7\)[/tex] is [tex]\(0 + 7 = 7\)[/tex].
The degree of the polynomial is the highest degree among its terms. Thus, the highest degree here is [tex]\(10\)[/tex] (from the term [tex]\(6 s t^9\)[/tex]).
### Conclusion
The statement that is true about the simplified polynomial is:
"It has 3 terms and a degree of 10."
So, the correct answer is: It has 3 terms and a degree of 10.
