Question

what is true about the completely simplified sum of the polynomials $3x^2y^2 - 2xy^5$ and $-3x^2y^2 + 3x^4y$?

the sum is a trinomial with a degree of 5.
the sum is a trinomial with a degree of 6.
the sum is a binomial with a degree of 5.
the sum is a binomial with a degree of 6.

Explanation:

Step1: Sum the polynomials

To find the sum of the polynomials \(3x^{2}y^{2}-2xy^{5}\) and \(-3x^{2}y^{2}+3x^{4}y\), we add like terms:

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Step2: Determine the type and degree

The simplified sum is \(-2xy^{5}+3x^{4}y\), which has two terms, so it is a binomial.
To find the degree of a term in a polynomial with multiple variables, we add the exponents of the variables.
For the term \(-2xy^{5}\), the degree is \(1 + 5=6\).
For the term \(3x^{4}y\), the degree is \(4+ 1 = 5\).
The degree of the polynomial is the highest degree of its terms, so the degree is 6.

Answer:

The sum is a binomial with a degree of 6.