Respuesta :
Answer:
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
To solve such problems we need to know about Trinomial.
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.
Given options to us are:
a.) [tex]\bold{3x^2y + 5x^3y + 6y^4}[/tex]
b.) [tex]\bold{6y^4 + 5x^3 + 1}[/tex]
c.) [tex]\bold{5xy - 5x^2y^2 + 7}[/tex]
d.) [tex]\bold{3y^3 + 3x^3y^3}[/tex]
To find
A fourth-degree polynomial is a polynomial whose highest order or degree or power is 4.
Now,
a.) [tex]\bold{3x^2y + 5x^3y + 6y^4}[/tex]
Yes, it is a fourth-degree trinomial, because [tex]\bold{6y^4}[/tex] has 4 as the highest power.
b.) [tex]\bold{6y^4 + 5x^3 + 1}[/tex]
Yes, it is a fourth-degree trinomial, because [tex]\bold{6y^4}[/tex] has 4 as the highest power.
c.) [tex]\bold{5xy - 5x^2y^2 + 7}[/tex]
No, it is not a fourth-degree trinomial, because none of the terms has 4 as the highest power.
d.) [tex]\bold{3y^3 + 3x^3y^3}[/tex]
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:
https://brainly.com/question/10273040