Answer :
To determine the degree of the polynomial [tex]\(28b^2c^3 + x + 66\)[/tex], we need to consider each term in the polynomial and find the term with the highest degree.
1. Identify each term:
- The polynomial has three terms: [tex]\(28b^2c^3\)[/tex], [tex]\(x\)[/tex], and [tex]\(66\)[/tex].
2. Determine the degree of each term:
- For [tex]\(28b^2c^3\)[/tex]: The degree of this term is found by adding the exponents of the variables [tex]\(b\)[/tex] and [tex]\(c\)[/tex]. The exponent of [tex]\(b\)[/tex] is 2, and the exponent of [tex]\(c\)[/tex] is 3. So, the total degree is [tex]\(2 + 3 = 5\)[/tex].
- For [tex]\(x\)[/tex]: The variable [tex]\(x\)[/tex] is implicitly raised to the power of 1, so the degree of [tex]\(x\)[/tex] is 1.
- For [tex]\(66\)[/tex]: This is a constant term, which means it does not involve any variables. The degree of a constant is always 0.
3. Find the highest degree:
- Compare the degrees of all the terms: 5, 1, and 0. The highest degree among these is 5.
Therefore, the degree of the polynomial [tex]\(28b^2c^3 + x + 66\)[/tex] is 5.
Degree = 5
1. Identify each term:
- The polynomial has three terms: [tex]\(28b^2c^3\)[/tex], [tex]\(x\)[/tex], and [tex]\(66\)[/tex].
2. Determine the degree of each term:
- For [tex]\(28b^2c^3\)[/tex]: The degree of this term is found by adding the exponents of the variables [tex]\(b\)[/tex] and [tex]\(c\)[/tex]. The exponent of [tex]\(b\)[/tex] is 2, and the exponent of [tex]\(c\)[/tex] is 3. So, the total degree is [tex]\(2 + 3 = 5\)[/tex].
- For [tex]\(x\)[/tex]: The variable [tex]\(x\)[/tex] is implicitly raised to the power of 1, so the degree of [tex]\(x\)[/tex] is 1.
- For [tex]\(66\)[/tex]: This is a constant term, which means it does not involve any variables. The degree of a constant is always 0.
3. Find the highest degree:
- Compare the degrees of all the terms: 5, 1, and 0. The highest degree among these is 5.
Therefore, the degree of the polynomial [tex]\(28b^2c^3 + x + 66\)[/tex] is 5.
Degree = 5
