Identify coefficients and the degrees of each term polynomial, and then find the degree of each polynomial.
a^3b^8c^2 - c^22 + a^5c^10
If a term contains only one variable, then its degree determines the degree of that term
e.g. -c^22 --- degree is 22
if the term contains multiple variables with exponents, then the degree of that term is the sum of those exponents.
e.g.
a^5c^10 has degree 15
To identify the coefficients and degrees of each term in the polynomial:
For the given polynomial, a^3b^8c^2 - c^22 + a^5c^10, let's break it down term by term.
Term 1: a^3b^8c^2
- Coefficient: The coefficient here is 1, which is the implicit coefficient when no explicit coefficient is mentioned.
- Degree: The degree of this term is found by adding the exponents of each variable: 3 + 8 + 2 = 13.
Term 2: - c^22
- Coefficient: The coefficient here is -1, which signifies a negative value.
- Degree: The degree of this term is 22 since there is only one variable (c) and it has an exponent of 22.
Term 3: + a^5c^10
- Coefficient: The coefficient here is 1, the implicit coefficient.
- Degree: The degree of this term is found by adding the exponents of each variable: 5 + 10 = 15.
Now, let's find the degree of the entire polynomial. The degree of a polynomial is the highest degree among all terms.
In this case, the highest degree is 22 (from the term - c^22). Therefore, the degree of the polynomial a^3b^8c^2 - c^22 + a^5c^10 is 22.