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Answer :
Sure! Let's find the degree of the given polynomial step by step.
The polynomial is:
[tex]\[
-v y^6 - 4 + 6 x^9 - 6 y^2 x^4 v^2
\][/tex]
To find the degree of a polynomial, we need to determine the degree of each term, which is the sum of the exponents of the variables in that term. The degree of the polynomial is the highest degree among its terms.
1. First Term: [tex]\(-v y^6\)[/tex]
- The exponent of [tex]\( v \)[/tex] is 1.
- The exponent of [tex]\( y \)[/tex] is 6.
- Total degree of this term is [tex]\( 1 + 6 = 7 \)[/tex].
2. Second Term: [tex]\(-4\)[/tex]
- This is a constant term, and the degree of any constant term is 0.
3. Third Term: [tex]\(6 x^9\)[/tex]
- The exponent of [tex]\( x \)[/tex] is 9.
- Total degree of this term is 9.
4. Fourth Term: [tex]\(-6 y^2 x^4 v^2\)[/tex]
- The exponent of [tex]\( y \)[/tex] is 2.
- The exponent of [tex]\( x \)[/tex] is 4.
- The exponent of [tex]\( v \)[/tex] is 2.
- Total degree of this term is [tex]\( 2 + 4 + 2 = 8 \)[/tex].
Now, we compare the degrees of all the terms:
- [tex]\(-v y^6\)[/tex] has a degree of 7.
- [tex]\(-4\)[/tex] has a degree of 0.
- [tex]\(6 x^9\)[/tex] has a degree of 9.
- [tex]\(-6 y^2 x^4 v^2\)[/tex] has a degree of 8.
The highest of these degrees is 9.
Therefore, the degree of the polynomial is 9.
The polynomial is:
[tex]\[
-v y^6 - 4 + 6 x^9 - 6 y^2 x^4 v^2
\][/tex]
To find the degree of a polynomial, we need to determine the degree of each term, which is the sum of the exponents of the variables in that term. The degree of the polynomial is the highest degree among its terms.
1. First Term: [tex]\(-v y^6\)[/tex]
- The exponent of [tex]\( v \)[/tex] is 1.
- The exponent of [tex]\( y \)[/tex] is 6.
- Total degree of this term is [tex]\( 1 + 6 = 7 \)[/tex].
2. Second Term: [tex]\(-4\)[/tex]
- This is a constant term, and the degree of any constant term is 0.
3. Third Term: [tex]\(6 x^9\)[/tex]
- The exponent of [tex]\( x \)[/tex] is 9.
- Total degree of this term is 9.
4. Fourth Term: [tex]\(-6 y^2 x^4 v^2\)[/tex]
- The exponent of [tex]\( y \)[/tex] is 2.
- The exponent of [tex]\( x \)[/tex] is 4.
- The exponent of [tex]\( v \)[/tex] is 2.
- Total degree of this term is [tex]\( 2 + 4 + 2 = 8 \)[/tex].
Now, we compare the degrees of all the terms:
- [tex]\(-v y^6\)[/tex] has a degree of 7.
- [tex]\(-4\)[/tex] has a degree of 0.
- [tex]\(6 x^9\)[/tex] has a degree of 9.
- [tex]\(-6 y^2 x^4 v^2\)[/tex] has a degree of 8.
The highest of these degrees is 9.
Therefore, the degree of the polynomial is 9.
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