Question

Which of the following expression(s) are fourth-degree trinomials? Select all that apply.

A. 3x²y + 5x3y + 6yA
B. 6y + 5x3 + 1
C. 5xy - 5x?y2 + 7
D. 3y2 + 3x3y2

Answer 1

Option C, 5xy - 5x²y² + 7, is the only fourth-degree trinomial among the given expressions because it contains a term with a combined degree of four (-5x²y²).

Step-by-step explanation:

The student asked to identify which expressions are fourth-degree trinomials. A fourth-degree trinomial is a polynomial with three terms where the highest degree of any term is four. Here's how to determine whether the given options are fourth-degree trinomials:

• A. 3x²y + 5x³y + 6y - This expression is not a fourth-degree trinomial because the highest degree of any term is three (as seen in 5x³y).
• B. 6y + 5x³ + 1 - This is not a fourth-degree trinomial for the same reason as option A.
• C. 5xy - 5x²y² + 7 - This expression is a fourth-degree trinomial. The term -5x²y² has a degree of four since the exponents add up to four (2 for x and 2 for y).
• D. 3y² + 3x³y² - This expression is not a fourth-degree trinomial, as it contains a term of fifth degree (3x³y² where the exponents add up to five).

Therefore, the only fourth-degree trinomial from the given options is C.

Answer 2

Options A and B are polynomial of the fourth degree

Step-by-step explanation:

In this problem, option

A. 3x2y + 5x3y + 6y4

Is a Polynomial of the fourth degree because of the 6y⁴ term which is the highest degree

Also the option

B. 6y4 + 5x3 + 1 has a 6y⁴ term which indicates that the polynomial is a fourth degree polynomial

What is the degree of a polynomial?

In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer