What Is True About The Sum Of The Two Polynomials?${ \begin{array}{l} 6s^2t - 2st^2 \ 4s^2t - 3st^2 \end{array} }$A. The Sum Is A Binomial With A Degree Of 2.B. The Sum Is A Binomial With A Degree Of 3.C. The Sum Is A Trinomial With A

Understanding Polynomials and Their Operations

Polynomials are algebraic expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication. When dealing with polynomials, it's essential to understand their properties and operations, including addition and subtraction. In this article, we will explore the sum of two given polynomials and determine the nature of the resulting expression.

The Given Polynomials

The two polynomials given are:

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

Adding the Polynomials

To find the sum of the two polynomials, we need to add their corresponding terms. This involves combining like terms, which are terms with the same variable and exponent.

{ \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

The resulting expression is $10s^2t - 5st^2$. To determine the nature of this expression, we need to examine its degree and the number of terms.

Degree of the Expression

The degree of a polynomial is the highest power of the variable in any of its terms. In this case, the highest power of $s$ and $t$ is 2. Therefore, the degree of the resulting expression is 2.

Number of Terms

The resulting expression has two terms: $10s^2t$ and $-5st^2$. Since it has two terms, it is not a binomial, which is a polynomial with two terms. However, it is not a trinomial either, which is a polynomial with three terms.

Conclusion

Based on the analysis, the sum of the two given polynomials is a binomial with a degree of 2. This is because it has two terms and the highest power of the variable is 2.

Answer Options

A. The sum is a binomial with a degree of 2. B. The sum is a binomial with a degree of 3. C. The sum is a trinomial with a degree of 2.

Correct Answer

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

Importance of Understanding Polynomial Operations

Understanding polynomial operations is crucial in algebra and mathematics. It helps in solving equations, graphing functions, and analyzing the behavior of polynomial expressions. In this article, we have demonstrated how to add two polynomials and determine the nature of the resulting expression. This knowledge can be applied to various mathematical problems and real-world applications.

Real-World Applications

Polynomial operations have numerous real-world applications, including:

• Computer Science: Polynomial operations are used in computer science to analyze and optimize algorithms.
• Engineering: Polynomial operations are used in engineering to design and analyze systems, such as electrical circuits and mechanical systems.
• Economics: Polynomial operations are used in economics to model and analyze economic systems.

Conclusion

In conclusion, the sum of the two given polynomials is a binomial with a degree of 2. Understanding polynomial operations is essential in mathematics and has numerous real-world applications. By applying the concepts learned in this article, readers can solve problems and analyze polynomial expressions with confidence.

Understanding Polynomials and Their Operations

Polynomials are algebraic expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication. When dealing with polynomials, it's essential to understand their properties and operations, including addition and subtraction. In this article, we will explore frequently asked questions about polynomials and their operations.

Q: What is a polynomial?

A: A polynomial is an algebraic expression consisting of variables and coefficients combined using addition, subtraction, and multiplication.

Q: What are the different types of polynomials?

A: There are several types of polynomials, including:

• Monomial: A polynomial with one term, such as $3x^2$.
• Binomial: A polynomial with two terms, such as $3x^2 + 2x$.
• Trinomial: A polynomial with three terms, such as $3x^2 + 2x + 1$.
• Polynomial: A polynomial with more than three terms.

Q: How do you add polynomials?

A: To add polynomials, you need to combine like terms, which are terms with the same variable and exponent. For example:

{ \begin{array}{l} (3x^2 + 2x) + (4x^2 + 3x) \\ = 3x^2 + 4x^2 + 2x + 3x \\ = 7x^2 + 5x \end{array} \}

Q: How do you subtract polynomials?

A: To subtract polynomials, you need to combine like terms, which are terms with the same variable and exponent. For example:

{ \begin{array}{l} (3x^2 + 2x) - (4x^2 + 3x) \\ = 3x^2 - 4x^2 + 2x - 3x \\ = -x^2 - x \end{array} \}

Q: What is the degree of a polynomial?

A: The degree of a polynomial is the highest power of the variable in any of its terms. For example, the degree of the polynomial $3x^2 + 2x$ is 2.

Q: How do you 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. For example, in the polynomial $3x^2 + 2x + 1$, the term with the highest power of $x$ is $3x^2$, which has a degree of 2.

Q: What is the difference between a polynomial and an algebraic expression?

A: A polynomial is a specific type of algebraic expression that consists of variables and coefficients combined using addition, subtraction, and multiplication. An algebraic expression, on the other hand, is a more general term that includes polynomials, rational expressions, and other types of expressions.

Q: How do you simplify a polynomial?

A: To simplify a polynomial, you need to combine like terms, which are terms with the same variable and exponent. For example:

{ \begin{array}{l} 3x^2 + 2x + 4x^2 \\ = 3x^2 + 4x^2 + 2x \\ = 7x^2 + 2x \end{array} \}

Q: What is the importance of understanding polynomial operations?

A: Understanding polynomial operations is crucial in algebra and mathematics. It helps in solving equations, graphing functions, and analyzing the behavior of polynomial expressions. In addition, polynomial operations have numerous real-world applications, including computer science, engineering, and economics.

Conclusion

In conclusion, understanding polynomial operations is essential in mathematics and has numerous real-world applications. By applying the concepts learned in this article, readers can solve problems and analyze polynomial expressions with confidence.