Determine if the expression 5, r, to the power 4 , minus, 4, r, to the power 4 , s, to the power 55r 4 −4r 4 s 5 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Question
Determine if the expression 5, r, to the power 4 , minus, 4, r, to the power 4 , s, to the power 55r 4 −4r 4 s 5 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Solution
The expression you provided seems to be a bit unclear, but I'll try to interpret it as best as I can.
If the expression is 5r^4 - 4r^4s^5, then yes, it is a polynomial. A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
The type of the polynomial is determined by the number of terms it has. In this case, there are two terms (5r^4 and -4r^4s^5), so it is a binomial.
The degree of a polynomial is the highest power of its variable(s). In this case, the highest power is 5 (from the term s^5), so the degree of the polynomial is 5.
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