Question

what is true about the sum of the two polynomials?
$6s^2t - 2st^2$
$4s^2t - 3st^2$
\bigcirc the sum is a binomial with a degree of 2.
\bigcirc the sum is a binomial with a degree of 3.
\bigcirc the sum is a trinomial with a degree of 2.
\bigcirc the sum is a trinomial with a degree of 3.

Explanation:

Step1: Add the two polynomials

To add the polynomials \(6s^{2}t - 2st^{2}\) and \(4s^{2}t - 3st^{2}\), we combine like terms.
For the \(s^{2}t\) terms: \(6s^{2}t+4s^{2}t=(6 + 4)s^{2}t = 10s^{2}t\)
For the \(st^{2}\) terms: \(-2st^{2}-3st^{2}=(-2-3)st^{2}=-5st^{2}\)
So the sum is \(10s^{2}t-5st^{2}\)

Step2: Determine the type and degree of the polynomial

The polynomial \(10s^{2}t - 5st^{2}\) 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 in the term.
For the term \(10s^{2}t\): the exponent of \(s\) is \(2\) and the exponent of \(t\) is \(1\), so the degree is \(2 + 1=3\)
For the term \(-5st^{2}\): the exponent of \(s\) is \(1\) and the exponent of \(t\) is \(2\), so the degree is \(1+2 = 3\)
The degree of the polynomial is the highest degree of its terms, so the degree of the polynomial \(10s^{2}t-5st^{2}\) is \(3\)

Answer:

The sum is a binomial with a degree of 3.