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:

Add the two polynomials

$$ (6s^2t - 2st^2) + (4s^2t - 3st^2) = (6 + 4)s^2t + (-2 - 3)st^2 = 10s^2t - 5st^2 $$

Determine the degree of the sum

$$ \text{Degree of } s^2t = 2 + 1 = 3,\quad \text{Degree of } st^2 = 1 + 2 = 3 \implies \text{Degree} = 3 $$

Classify the polynomial by terms

$$ 10s^2t - 5st^2 \text{ has exactly two terms} \implies \text{Binomial} $$

Answer:

• The sum is a binomial with a degree of 2.
• The sum is a binomial with a degree of 3. (Correct answer)
• The sum is a trinomial with a degree of 2.
• The sum is a trinomial with a degree of 3.