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Answer :
Sure, let's break it down step-by-step:
1. Find the degree of the term [tex]\( -6x^9 \)[/tex]:
- The degree of a term in a polynomial is determined by the exponent of the variable [tex]\( x \)[/tex].
- For the term [tex]\( -6x^9 \)[/tex], the exponent of [tex]\( x \)[/tex] is 9.
- So, the degree of the term [tex]\( -6x^9 \)[/tex] is [tex]\( 9 \)[/tex].
2. Find the degree of the term [tex]\( -4x^8 \)[/tex]:
- The degree of the term is again determined by the exponent of the variable [tex]\( x \)[/tex].
- For the term [tex]\( -4x^8 \)[/tex], the exponent of [tex]\( x \)[/tex] is 8.
- So, the degree of the term [tex]\( -4x^8 \)[/tex] is [tex]\( 8 \)[/tex].
3. Find the degree of the term [tex]\( 1x^6 \)[/tex]:
- The degree of the term is determined by the exponent of the variable [tex]\( x \)[/tex].
- For the term [tex]\( 1x^6 \)[/tex], the exponent of [tex]\( x \)[/tex] is 6.
- So, the degree of the term [tex]\( 1x^6 \)[/tex] is [tex]\( 6 \)[/tex].
4. Find the degree of the term 6:
- The term 6 is a constant term. A constant term is any term that does not contain a variable.
- The degree of a constant term is [tex]\( 0 \)[/tex] because it can be thought of as [tex]\( 6x^0 \)[/tex].
- So, the degree of the term [tex]\( 6 \)[/tex] is [tex]\( 0 \)[/tex].
5. Find the degree of the polynomial [tex]\( -6x^9 - 4x^8 + 1x^6 + 6 \)[/tex]:
- The degree of a polynomial is the highest degree of any term in the polynomial.
- In this polynomial, the degrees of the terms are [tex]\( 9 \)[/tex], [tex]\( 8 \)[/tex], [tex]\( 6 \)[/tex], and [tex]\( 0 \)[/tex].
- The highest of these degrees is [tex]\( 9 \)[/tex].
- So, the degree of the polynomial [tex]\( -6x^9 - 4x^8 + 1x^6 + 6 \)[/tex] is [tex]\( 9 \)[/tex].
Here are the answers summarized:
- Degree of the term [tex]\( -6x^9 \)[/tex]: [tex]\( 9 \)[/tex]
- Degree of the term [tex]\( -4x^8 \)[/tex]: [tex]\( 8 \)[/tex]
- Degree of the term [tex]\( 1x^6 \)[/tex]: [tex]\( 6 \)[/tex]
- Degree of the term 6: [tex]\( 0 \)[/tex]
- Degree of the polynomial [tex]\( -6x^9 - 4x^8 + 1x^6 + 6 \)[/tex]: [tex]\( 9 \)[/tex]
1. Find the degree of the term [tex]\( -6x^9 \)[/tex]:
- The degree of a term in a polynomial is determined by the exponent of the variable [tex]\( x \)[/tex].
- For the term [tex]\( -6x^9 \)[/tex], the exponent of [tex]\( x \)[/tex] is 9.
- So, the degree of the term [tex]\( -6x^9 \)[/tex] is [tex]\( 9 \)[/tex].
2. Find the degree of the term [tex]\( -4x^8 \)[/tex]:
- The degree of the term is again determined by the exponent of the variable [tex]\( x \)[/tex].
- For the term [tex]\( -4x^8 \)[/tex], the exponent of [tex]\( x \)[/tex] is 8.
- So, the degree of the term [tex]\( -4x^8 \)[/tex] is [tex]\( 8 \)[/tex].
3. Find the degree of the term [tex]\( 1x^6 \)[/tex]:
- The degree of the term is determined by the exponent of the variable [tex]\( x \)[/tex].
- For the term [tex]\( 1x^6 \)[/tex], the exponent of [tex]\( x \)[/tex] is 6.
- So, the degree of the term [tex]\( 1x^6 \)[/tex] is [tex]\( 6 \)[/tex].
4. Find the degree of the term 6:
- The term 6 is a constant term. A constant term is any term that does not contain a variable.
- The degree of a constant term is [tex]\( 0 \)[/tex] because it can be thought of as [tex]\( 6x^0 \)[/tex].
- So, the degree of the term [tex]\( 6 \)[/tex] is [tex]\( 0 \)[/tex].
5. Find the degree of the polynomial [tex]\( -6x^9 - 4x^8 + 1x^6 + 6 \)[/tex]:
- The degree of a polynomial is the highest degree of any term in the polynomial.
- In this polynomial, the degrees of the terms are [tex]\( 9 \)[/tex], [tex]\( 8 \)[/tex], [tex]\( 6 \)[/tex], and [tex]\( 0 \)[/tex].
- The highest of these degrees is [tex]\( 9 \)[/tex].
- So, the degree of the polynomial [tex]\( -6x^9 - 4x^8 + 1x^6 + 6 \)[/tex] is [tex]\( 9 \)[/tex].
Here are the answers summarized:
- Degree of the term [tex]\( -6x^9 \)[/tex]: [tex]\( 9 \)[/tex]
- Degree of the term [tex]\( -4x^8 \)[/tex]: [tex]\( 8 \)[/tex]
- Degree of the term [tex]\( 1x^6 \)[/tex]: [tex]\( 6 \)[/tex]
- Degree of the term 6: [tex]\( 0 \)[/tex]
- Degree of the polynomial [tex]\( -6x^9 - 4x^8 + 1x^6 + 6 \)[/tex]: [tex]\( 9 \)[/tex]
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