Chapter 8.1, Problem 1CYU

To determine

To find: Whether the expression $7ab+6b^2-2a^3$ is a polynomial or not. If it is a polynomial, find the degree and determine if it is a monomial, binomial, or trinomial.

Answer to Problem 1CYU

Yes, it is a polynomial

Degree of the polynomial is $3$

It is a trinomial

Explanation of Solution

Given:

  $7ab+6b^2-2a^3$

Calculation:

The given expression is $7ab+6b^2-2a^3$

The exponent of a polynomial must be a whole number. For a polynomial, the exponent can never be negative, square root, any fractional number and no variable should be in the denominator.

Here all the exponents are whole numbers and the polynomial satisfies all the above conditions as well.

Hence, it is a polynomial.

The degree of a polynomial is the highest exponent. So, the degree is $3$

And since, it has three terms. So, it is a trinomial.