Question

Determine the type and degree of each of the following polynomial expressions

9x⁴y⁹x⁴-3x²+7x⁵19a⁶b²+8ab³c-27a⁷​

Answer 1

Polynomial expressions are classified as binomials or trinomials based on the number of terms, and their degree is based on the highest exponent sum of the variables. The given expressions have degrees of 5, 5, and 7, correspondingly.

Step-by-step explanation:

To determine the type and degree of each polynomial expression, we will look at the expressions one by one:

1. For the expression 9x⁴y¹, this is a binomial because it consists of two terms and the degree of this polynomial is 5 (sum of the powers of x and y in the term with the highest combined degree).
2. The second expression looks like it might have some typos, but if we consider x⁴-3x²+7x⁵, this is a trinomial with three terms, and the degree is 5, which is the highest power of x present in the polynomial.
3. Lastly, the expression 19a⁶b²+8ab³c-27a⁷ is a trinomial, and its degree is 7, from the term with the highest power of a, which is a⁷.

Note that the type of polynomial is determined by the number of terms: binomials have two terms, and trinomials have three terms. The degree of a polynomial is the highest sum of the exponents of the variables in any one term.