Question

determine if the expression $-4bc^4 + 10c^2 + 2b$ is a polynomial or not. if it is a polynomial, state the type and degree of the polynomial.
answer
the given expression represents a polynomial. the polynomial is a
trinomial
and has a degree of
10
.
options for type: monomial, binomial, trinomial, none of the above

Explanation:

Step1: Verify polynomial validity

A polynomial has non-negative integer exponents on variables. For $-4d^6c^4 + 10c^2 + 2b$, all exponents (6,4,2,1) are non-negative integers, so it is a polynomial.

Step2: Classify polynomial type

Count the number of terms: $-4d^6c^4$, $10c^2$, $2b$ are 3 distinct terms. A 3-term polynomial is a trinomial.

Step3: Calculate polynomial degree

Find the degree of each term:

• Degree of $-4d^6c^4$: $6+4=10$
• Degree of $10c^2$: $2$
• Degree of $2b$: $1$

The highest degree is 10.

Answer:

The expression is a polynomial. It is a trinomial with a degree of 10.