Question

Classify the polynomial A⁵ + B² + A²B² by its degree and the number of terms.

a. Quadratic trinomial
b. Cubic binomial
c. Quartic monomial
d. Quintic trinomial

Answer 1

The polynomial A⁵ + B² + A²B² is classified as a quintic trinomial because it has a highest degree of 5 and contains three terms.

Step-by-step explanation:

The polynomial A⁵ + B² + A²B² is classified by both its degree and the number of terms it contains. To classify it:

• Determine the polynomial's degree by looking for the highest sum of exponents in a single term, which for A⁵ + B² + A²B² is 5 (from the term A⁵).
• Count the number of terms, which in the given polynomial is 3 (A⁵, B², and A²B²).

With the highest degree being 5 and three terms present, we classify the polynomial as a quintic trinomial.