Frequently Asked Questions About the Sum of Two Polynomials

Oct 13, 2025 by miodeya.com 3 views

What is True About the Sum of the Two Polynomials?

Understanding Polynomials and Their Operations

Polynomials are algebraic expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. They are denoted by letters such as $a$ , $b$ , $c$ , etc., and can be represented in various forms, including monomials, binomials, and trinomials. In this article, we will explore the sum of two polynomials and determine the nature of the resulting expression.

The Sum of Two Polynomials

Given two polynomials:

\begin{array}{l} 6s^2t - 2st^2 \\ 4s^2t - 3st^2 \end{array}

We are asked to find the sum of these two polynomials. To do this, we will combine like terms, which involves adding or subtracting the coefficients of the same variables.

Combining Like Terms

To combine like terms, we need to identify the terms with the same variables and coefficients. In this case, we have two terms with the variable $s^2t$ and two terms with the variable $st^2$ .

The sum of the two polynomials is:

\begin{array}{l} (6s^2t - 2st^2) + (4s^2t - 3st^2) \\ = 6s^2t + 4s^2t - 2st^2 - 3st^2 \\ = 10s^2t - 5st^2 \end{array}

Analyzing the Resulting Expression

Now that we have found the sum of the two polynomials, let's analyze the resulting expression. We have a term with the variable $s^2t$ and a term with the variable $st^2$ . Since the degree of a polynomial is determined by the highest power of the variable, we can conclude that the degree of the resulting expression is 2.

Conclusion

Based on our analysis, we can conclude that the sum of the two polynomials is a binomial with a degree of 2. This is because the resulting expression has two terms with the same variable and a degree of 2.

Answer

The correct answer is:

A. The sum is a binomial with a degree of 2.

Discussion

This problem requires a basic understanding of polynomials and their operations. The student should be able to identify like terms, combine them, and determine the degree of the resulting expression. This problem is relevant to the topic of algebra and is a fundamental concept in mathematics.

Additional Examples

Here are a few additional examples to illustrate the concept of combining like terms and determining the degree of a polynomial:

$(2x^2 + 3x - 4) + (x^2 - 2x + 1)$
$(3y^2 - 2y + 1) + (2y^2 + 3y - 4)$

In each of these examples, the student should be able to combine like terms and determine the degree of the resulting expression.

Conclusion

In conclusion, the sum of two polynomials is a binomial with a degree of 2. This is because the resulting expression has two terms with the same variable and a degree of 2. The student should be able to identify like terms, combine them, and determine the degree of the resulting expression. This problem is relevant to the topic of algebra and is a fundamental concept in mathematics.
Frequently Asked Questions About the Sum of Two Polynomials

Q: What is the sum of the two polynomials $6s^2t - 2st^2$ and $4s^2t - 3st^2$ ?

A: The sum of the two polynomials is $10s^2t - 5st^2$ .

Q: What is the degree of the resulting expression?

A: The degree of the resulting expression is 2.

Q: Why is the resulting expression a binomial?

A: The resulting expression is a binomial because it has two terms with the same variable and a degree of 2.

Q: How do I combine like terms?

A: To combine like terms, you need to identify the terms with the same variables and coefficients. Then, you can add or subtract the coefficients of the same variables.

Q: What are like terms?

A: Like terms are terms with the same variables and coefficients. For example, $2x^2$ and $3x^2$ are like terms because they have the same variable $x$ and the same degree.

Q: How do I determine the degree of a polynomial?

A: To determine the degree of a polynomial, you need to identify the term with the highest power of the variable. The degree of the polynomial is the power of the variable in that term.

Q: What is the difference between a monomial, binomial, and trinomial?

A: A monomial is a polynomial with one term. A binomial is a polynomial with two terms. A trinomial is a polynomial with three terms.

Q: Can you give an example of a monomial, binomial, and trinomial?

A: Here are some examples:

Monomial: $3x^2$
Binomial: $2x^2 + 3x$
Trinomial: $2x^2 + 3x - 4$

Q: How do I add or subtract polynomials?

A: To add or subtract polynomials, you need to combine like terms. This involves adding or subtracting the coefficients of the same variables.

Q: Can you give an example of adding two polynomials?

A: Here is an example:

(2x^2 + 3x - 4) + (x^2 - 2x + 1)

To add these two polynomials, you need to combine like terms:

2x^2 + x^2 = 3x^2

3x - 2x = x

-4 + 1 = -3

So, the resulting expression is:

3x^2 + x - 3

Q: Can you give an example of subtracting two polynomials?

A: Here is an example:

(2x^2 + 3x - 4) - (x^2 - 2x + 1)

To subtract these two polynomials, you need to combine like terms:

2x^2 - x^2 = x^2

3x + 2x = 5x

-4 - 1 = -5

So, the resulting expression is:

x^2 + 5x - 5

Conclusion