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Answer :
To determine the degree of a polynomial, you look for the highest exponent of the variable within the polynomial.
Let's analyze the given polynomial:
[tex]\[ 4x + 9x^5 + 9 + 3x^4 \][/tex]
Step-by-step:
1. Identify the terms and their exponents:
- The term [tex]\(4x\)[/tex] has a variable [tex]\(x\)[/tex] with an exponent of 1.
- The term [tex]\(9x^5\)[/tex] has a variable [tex]\(x\)[/tex] with an exponent of 5.
- The constant term [tex]\(9\)[/tex] can be thought of as [tex]\(9x^0\)[/tex] (since any non-zero number to the power of zero is 1), so it has an exponent of 0.
- The term [tex]\(3x^4\)[/tex] has a variable [tex]\(x\)[/tex] with an exponent of 4.
2. List the exponents: We have the exponents 1, 5, 0, and 4 from terms [tex]\(4x\)[/tex], [tex]\(9x^5\)[/tex], the constant 9, and [tex]\(3x^4\)[/tex] respectively.
3. Find the highest exponent: The highest exponent among these is 5.
Therefore, the degree of the polynomial [tex]\(4x + 9x^5 + 9 + 3x^4\)[/tex] is 5.
Let's analyze the given polynomial:
[tex]\[ 4x + 9x^5 + 9 + 3x^4 \][/tex]
Step-by-step:
1. Identify the terms and their exponents:
- The term [tex]\(4x\)[/tex] has a variable [tex]\(x\)[/tex] with an exponent of 1.
- The term [tex]\(9x^5\)[/tex] has a variable [tex]\(x\)[/tex] with an exponent of 5.
- The constant term [tex]\(9\)[/tex] can be thought of as [tex]\(9x^0\)[/tex] (since any non-zero number to the power of zero is 1), so it has an exponent of 0.
- The term [tex]\(3x^4\)[/tex] has a variable [tex]\(x\)[/tex] with an exponent of 4.
2. List the exponents: We have the exponents 1, 5, 0, and 4 from terms [tex]\(4x\)[/tex], [tex]\(9x^5\)[/tex], the constant 9, and [tex]\(3x^4\)[/tex] respectively.
3. Find the highest exponent: The highest exponent among these is 5.
Therefore, the degree of the polynomial [tex]\(4x + 9x^5 + 9 + 3x^4\)[/tex] is 5.
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