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
Find the degree show all work: a^3b^8c^2 - c^22 + a^5c^10
To identify the coefficients and degrees of each term in the polynomial, we first need to understand the format of a term in a polynomial. In general, a term in a polynomial has the form:
coefficient * variable term
Here, the coefficient is a numerical value that multiplies the variable term. The variable term consists of variables raised to various powers.
Now, let's break down the given polynomial:
a^3b^8c^2 - c^22 + a^5c^10
The first term is a^3b^8c^2:
- The coefficient is 1 (since there is no explicit numerical coefficient mentioned).
- The variable term is a^3b^8c^2.
- The degree of the term is the sum of the exponents of all the variables; in this case, it is 3 + 8 + 2 = 13.
The second term is -c^22:
- The coefficient is -1 (since there is a negative sign in front of the term).
- The variable term is c^22.
- The degree of this term is 22.
The third term is a^5c^10:
- The coefficient is 1 (since there is no explicit numerical coefficient mentioned).
- The variable term is a^5c^10.
- The degree of this term is 5 + 10 = 15.
To find the degree of the polynomial, we consider the highest degree among all the terms, which is 15 in this case. Therefore, the degree of the polynomial is 15.