Question

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

Explanation:

Step1: Add like terms

To find the sum of the two polynomials, we add the coefficients of the 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 number of terms and degree

The sum has two terms, so it is a binomial. To find the degree, we look at the exponents of each term. For \(10s^{2}t\), the sum of exponents is \(2 + 1=3\). For \(-5st^{2}\), the sum of exponents is \(1+2 = 3\). So the degree of the polynomial is 3.

Answer:

The sum is a binomial with a degree of 3.