Which of the following expression(s) are fourth-degree trinomials? Select all that apply.
A. 3x2y + 5x3y + 6y4
B. 6y4 + 5x3 + 1
C. 5xy − 5x2y2 + 7
D. 3y3 + 3x3y3

To solve such problems we need to know about Trinomial.

A trinomial is a polynomial whose is the sum of three monomials, therefore, it will be the sum of three, unlike terms.

{Note: A trinomial is always a polynomial while a polynomial is not necessarily trinomial}

Only options a and b are correct.

a.)

b.)

c.)

d.)

A fourth-degree polynomial is a polynomial whose highest order or degree or power is 4.

Now,

a.)

Yes, it is a fourth-degree trinomial, because has 4 as the highest power.

b.)

Yes, it is a fourth-degree trinomial, because has 4 as the highest power.

c.)

No, it is not a fourth-degree trinomial, because none of the terms has 4 as the highest power.

d.)

No, it is not a fourth-degree trinomial, because none of the terms has 4 as the highest power. Also, it has only two monomials.

Hence, only options a and b are correct.

Learn more about Trinomial:

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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