Which Represents The Polynomial Written In Standard Form?A. { -2m^4 - 6m^2 + 4m + 9$}$ B. ${ 2m^4 - 6m^2 - 4m + 9\$} C. { -6m^2 + 4m - 2m^4$}$ D. ${ 4m - 2m^4 - 6m^2 + 9\$} E. ${ 9 + 4m + 2m^4 - 6m^2\$}

**Which Represents the Polynomial Written in Standard Form?** ===========================================================

Understanding Polynomials in Standard Form

A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. In the standard form of a polynomial, the terms are arranged in descending order of the exponents of the variables. This means that the term with the highest exponent comes first, followed by the terms with lower exponents.

Key Characteristics of Standard Form

• The terms are arranged in descending order of the exponents of the variables.
• The term with the highest exponent comes first.
• The coefficients of the terms are written in front of the variables.

Analyzing the Options

Let's analyze each option to determine which one represents the polynomial written in standard form.

Option A: ${-2m^4 - 6m^2 + 4m + 9}$

This option has the term with the highest exponent, ${-2m^4}$, coming first. However, the term ${-6m^2}$ comes before the term ${4m}$. In standard form, the term with the lower exponent should come after the term with the higher exponent. Therefore, this option does not represent the polynomial written in standard form.

Option B: ${2m^4 - 6m^2 - 4m + 9}$

This option has the term with the highest exponent, ${2m^4}$, coming first. The terms ${-6m^2}$ and ${-4m}$ come next, followed by the constant term ${9}$. This option meets the criteria for standard form, as the terms are arranged in descending order of the exponents of the variables.

Option C: ${-6m^2 + 4m - 2m^4}$

This option has the term with the highest exponent, ${-2m^4}$, coming last. The terms ${-6m^2}$ and ${4m}$ come first, followed by the term with the highest exponent. This option does not meet the criteria for standard form, as the terms are not arranged in descending order of the exponents of the variables.

Option D: ${4m - 2m^4 - 6m^2 + 9}$

This option has the term with the highest exponent, ${-2m^4}$, coming second. The term ${4m}$ comes first, followed by the term with the highest exponent. The terms ${-6m^2}$ and ${9}$ come last. This option does not meet the criteria for standard form, as the terms are not arranged in descending order of the exponents of the variables.

Option E: ${9 + 4m + 2m^4 - 6m^2}$

This option has the constant term ${9}$ coming first. The term ${4m}$ comes next, followed by the term with the highest exponent, ${2m^4}$. The term ${-6m^2}$ comes last. This option does not meet the criteria for standard form, as the terms are not arranged in descending order of the exponents of the variables.

Conclusion

Based on the analysis of each option, the correct answer is Option B: ${2m^4 - 6m^2 - 4m + 9}$. This option meets the criteria for standard form, as the terms are arranged in descending order of the exponents of the variables.

Key Takeaways

• A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
• In the standard form of a polynomial, the terms are arranged in descending order of the exponents of the variables.
• The term with the highest exponent comes first, followed by the terms with lower exponents.
• The coefficients of the terms are written in front of the variables.

Practice Problems

1. Which of the following polynomials is written in standard form? ${3x^2 + 2x - 4}$ ${2x - 3x^2 - 4}$ ${4 - 2x^2 + 3x}$ ${3x^2 - 2x + 4}$ ${-4 + 2x^2 - 3x}$
2. Which of the following polynomials is not written in standard form? ${x^2 + 2x - 3}$ ${2x^2 - 3x + 1}$ ${-3x^2 + 2x - 1}$ ${3x^2 - 2x + 1}$ ${1 - 2x^2 + 3x}$

Answer Key

1. ${3x^2 + 2x - 4}$
2. ${1 - 2x^2 + 3x}$