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Answer :
To determine the degree of a polynomial, you need to identify the highest power of the variable [tex]\(x\)[/tex] in the expression. Let's break down the polynomial [tex]\(-9 + 4x + 2x^2 - 2x^6\)[/tex] term by term:
1. The term [tex]\(-9\)[/tex] is actually [tex]\(x^0\)[/tex], so its degree is 0.
2. The term [tex]\(4x\)[/tex] is [tex]\(4x^1\)[/tex], so its degree is 1.
3. The term [tex]\(2x^2\)[/tex] has the degree 2 because it is written as [tex]\(x^2\)[/tex].
4. The term [tex]\(-2x^6\)[/tex] has the degree 6 because it is [tex]\(x^6\)[/tex].
Among these terms, the highest degree is 6 from the term [tex]\(-2x^6\)[/tex].
Therefore, the degree of the polynomial [tex]\(-9 + 4x + 2x^2 - 2x^6\)[/tex] is 6.
1. The term [tex]\(-9\)[/tex] is actually [tex]\(x^0\)[/tex], so its degree is 0.
2. The term [tex]\(4x\)[/tex] is [tex]\(4x^1\)[/tex], so its degree is 1.
3. The term [tex]\(2x^2\)[/tex] has the degree 2 because it is written as [tex]\(x^2\)[/tex].
4. The term [tex]\(-2x^6\)[/tex] has the degree 6 because it is [tex]\(x^6\)[/tex].
Among these terms, the highest degree is 6 from the term [tex]\(-2x^6\)[/tex].
Therefore, the degree of the polynomial [tex]\(-9 + 4x + 2x^2 - 2x^6\)[/tex] is 6.
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