According to Paul's Online Math Notes at Lamar University, a polynomial is defined as an algebraic expression whose terms consist of coefficients multiplied by variables raised to non-negative integer powers. And the degree of a polynomial is simply the highest exponent among its terms.

Polynomials are the fundamental concepts in algebra, and problems like what is true about the sum of the two polynomials 6s²t - 2st² and 4s²t - 3st²? are common in finals, assignments, and competitive tests. In this article, we'll break it down step by step, simplify the sum, and dive into degree and type of polynomial. This will not only help you solve the problem, you'll have deep knowledge around it.

Q. What is true about the sum of the two polynomials 6s²t - 2st² and 4s²t - 3st²?

Here's the step by step solution:-

Step 1: Write the Given Polynomials

We are asked to add the following:

• $6s²t - 2st²$
• $4s²t - 3st²$

Step 2: Combine Like Terms

When adding polynomials, combine terms with the same variables and exponents:

$$(6s²t - 2st²) + (4s²t - 3st²)$$

• Combine $6s²t + 4s²t = 10s²t$
• Combine $-2st² - 3st² = -5st²$

So the result is:

$$10s²t - 5st²$$

Step 3: Identify the Type of Polynomial

• The expression has two terms → it is a binomial.

Step 4: Find the Degree of the Polynomial

The degree of a polynomial is the highest sum of exponents in any term.

• Term $10s²t$: degree = $2 + 1 = 3$
• Term $-5st²$: degree = $1 + 2 = 3$

Hence, both terms have degree 3 → The polynomial's degree is 3.

Final Answer

The sum of $6s²t - 2st²$ and $4s²t - 3st²$ is:

$$10s²t - 5st²$$

Thus it is a binomial of degree 3.

Why This Question Is Important

• Helps practice combining like terms.
• Reinforces the difference between binomial, trinomial, and polynomial.
• Strengthens understanding of degree of a polynomial.

Practice Question

Try this yourself:

$$(5x³y - 2xy²) + (3x³y - xy²)$$

• What is the simplified form?
• Is it a binomial or trinomial?
• What is its degree?

(Answer: $8x³y - 3xy²$, binomial, degree 4.)

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