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Answer :
To determine the degree of the polynomial [tex]\(3x^9 + 4 - 11u^2x^4y^2 - yu^5\)[/tex], we need to find the degree of each term and then identify the largest one.
1. Identify each term:
- The first term is [tex]\(3x^9\)[/tex].
- The second term is a constant, [tex]\(4\)[/tex].
- The third term is [tex]\(-11u^2x^4y^2\)[/tex].
- The fourth term is [tex]\(-yu^5\)[/tex].
2. Calculate the degree of each term:
- The degree of the term [tex]\(3x^9\)[/tex] is 9, because the largest exponent on any variable in that term is 9 (from [tex]\(x^9\)[/tex]).
- The degree of the constant term [tex]\(4\)[/tex] is 0, as it has no variable.
- The degree of the term [tex]\(-11u^2x^4y^2\)[/tex] is [tex]\(2 + 4 + 2 = 8\)[/tex], by adding the exponents of the variables [tex]\(u\)[/tex], [tex]\(x\)[/tex], and [tex]\(y\)[/tex].
- The degree of the term [tex]\(-yu^5\)[/tex] is [tex]\(1 + 5 = 6\)[/tex], by adding the exponents of [tex]\(y\)[/tex] and [tex]\(u\)[/tex].
3. Find the highest degree:
- Among the degrees, 9, 8, 6, and 0, the largest is 9.
Therefore, the degree of the polynomial is 9.
1. Identify each term:
- The first term is [tex]\(3x^9\)[/tex].
- The second term is a constant, [tex]\(4\)[/tex].
- The third term is [tex]\(-11u^2x^4y^2\)[/tex].
- The fourth term is [tex]\(-yu^5\)[/tex].
2. Calculate the degree of each term:
- The degree of the term [tex]\(3x^9\)[/tex] is 9, because the largest exponent on any variable in that term is 9 (from [tex]\(x^9\)[/tex]).
- The degree of the constant term [tex]\(4\)[/tex] is 0, as it has no variable.
- The degree of the term [tex]\(-11u^2x^4y^2\)[/tex] is [tex]\(2 + 4 + 2 = 8\)[/tex], by adding the exponents of the variables [tex]\(u\)[/tex], [tex]\(x\)[/tex], and [tex]\(y\)[/tex].
- The degree of the term [tex]\(-yu^5\)[/tex] is [tex]\(1 + 5 = 6\)[/tex], by adding the exponents of [tex]\(y\)[/tex] and [tex]\(u\)[/tex].
3. Find the highest degree:
- Among the degrees, 9, 8, 6, and 0, the largest is 9.
Therefore, the degree of the polynomial is 9.
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