Let's analyze the polynomial [tex]\(12x^4y^5 + xy^6\)[/tex] step-by-step:
1. Identify the degrees of individual terms:
- For the term [tex]\(12x^4y^5\)[/tex]:
- The exponent of [tex]\(x\)[/tex] is 4.
- The exponent of [tex]\(y\)[/tex] is 5.
- The degree of this term is the sum of the exponents: [tex]\(4 + 5 = 9\)[/tex].
- For the term [tex]\(xy^6\)[/tex]:
- The exponent of [tex]\(x\)[/tex] is 1 (implicitly given).
- The exponent of [tex]\(y\)[/tex] is 6.
- The degree of this term is the sum of the exponents: [tex]\(1 + 6 = 7\)[/tex].
2. Determine the degree of the polynomial:
- The degree of a polynomial is the highest degree of its individual terms.
- Here, the degrees of the terms are 9 and 7.
- Thus, the maximum degree of the polynomial [tex]\(12x^4y^5 + xy^6\)[/tex] is [tex]\( \max(9, 7) = 9\)[/tex].
Therefore, the degree of the polynomial [tex]\(12x^4y^5 + xy^6\)[/tex] is 9.
