Determine if the expression minus, d, squared, plus, 8, c, to the power 5−d 2 +8c 5 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Question
Determine if the expression minus, d, squared, plus, 8, c, to the power 5−d 2 +8c 5 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Solution
The expression given is -d^2 + 8c^5.
First, let's understand what a polynomial is. 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).
Looking at the expression -d^2 + 8c^5, we can see that it is indeed a polynomial. It consists of two terms, each containing a variable raised to a power.
The type of a polynomial is determined by the number of terms it has. Since our expression has two terms, it is a binomial.
The degree of a polynomial is the highest power of its variable(s). In our expression, the highest power is 5 (in the term 8c^5), so the degree of the polynomial is 5.
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