Question

PLS HELP ALGEBRA 2 QUESTION ASAP 5 STARS AND BRAINLIEST what type of polynomial is 7Dy%2B3x%5E%7B2%7Dy%2B4xy-6y%2B1" id="TexFormula1" title="-5x^{4}y+3x^{2}y+4xy-6y+1" alt="-5x^{4}y+3x^{2}y+4xy-6y+1" align="absmiddle" class="latex-formula"> and show your work.

Answer 1

Answer:

Binomial

Step-by-step explanation:

Edited to add:

It can also be called a binomial because there are 2 unlike terms x and y. I'm not sure what you are studying, so it may be better to go with binomial. The Quartic is when you are looking at the degree of a single term polynomial.

You can name a polynomial based on terms, or based on degrees.

If it's based on degree it would be bi-quadratic, because it's ^4 and you have 2 different terms. If you're looking at terms it would be binomial because you have x and y to solve for.

The degree of terms is a major deciding factor whether an equation is homogeneous or not. A polynomial of more that one variable is said to be homogeneous if the degree of each term is the same. For example, 2x^7+5x^5y^2-3x^4y^3+4x^2y^5 is a homogeneous polynomial of degree 7 in x and y.

You have a 4 term polynomial with 2 variables x and y. The highest degree in your equation is 5 (4 + 1 from the first term) so the degree of the multivariable polynomial expression is 6.

All these answers are correct, it just depends what you're studying. If some of these words are new, and others you recognize from class or your book, go with the one that looks familiar.

Answer 2

Answer: 5th degree polynomial (quintic polynomial)

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Explanation:

5x^4y is the same as 5x^4y^1. The exponents 4 and 1 sum to 4+1 = 5

The term 3x^2y, or 3x^2y^1, has the exponents add to 3

The term 4xy has the exponents add to 2

The largest sum of exponents is 5, so we have a 5th degree polynomial

This is known as a quintic polynomial

Note: the degree of the polynomial is equal to the largest sum of exponents for each term, so the degree is 5.