Answer :
To find the degree of the polynomial [tex]\(9x^6 + 7x^5 + 5\)[/tex], we need to identify the highest power of the variable [tex]\(x\)[/tex] present in the polynomial. Here's a step-by-step breakdown:
1. Identify the Terms: The polynomial is made up of three terms: [tex]\(9x^6\)[/tex], [tex]\(7x^5\)[/tex], and [tex]\(5\)[/tex].
2. Find the Exponents: Look at the exponent (power) of [tex]\(x\)[/tex] in each term:
- In [tex]\(9x^6\)[/tex], the exponent is 6.
- In [tex]\(7x^5\)[/tex], the exponent is 5.
- In [tex]\(5\)[/tex], there is no [tex]\(x\)[/tex], so the exponent is considered to be 0.
3. Determine the Highest Exponent: Compare the exponents found in the terms to identify the highest one. The highest power of [tex]\(x\)[/tex] is 6, which comes from the term [tex]\(9x^6\)[/tex].
4. Conclusion: The degree of the polynomial is the highest exponent of [tex]\(x\)[/tex] in the polynomial, which is 6.
Therefore, the degree of the polynomial [tex]\(9x^6 + 7x^5 + 5\)[/tex] is 6.
1. Identify the Terms: The polynomial is made up of three terms: [tex]\(9x^6\)[/tex], [tex]\(7x^5\)[/tex], and [tex]\(5\)[/tex].
2. Find the Exponents: Look at the exponent (power) of [tex]\(x\)[/tex] in each term:
- In [tex]\(9x^6\)[/tex], the exponent is 6.
- In [tex]\(7x^5\)[/tex], the exponent is 5.
- In [tex]\(5\)[/tex], there is no [tex]\(x\)[/tex], so the exponent is considered to be 0.
3. Determine the Highest Exponent: Compare the exponents found in the terms to identify the highest one. The highest power of [tex]\(x\)[/tex] is 6, which comes from the term [tex]\(9x^6\)[/tex].
4. Conclusion: The degree of the polynomial is the highest exponent of [tex]\(x\)[/tex] in the polynomial, which is 6.
Therefore, the degree of the polynomial [tex]\(9x^6 + 7x^5 + 5\)[/tex] is 6.
