Which Terms Could Be Used As The Last Term Of The Expression Below To Create A Polynomial Written In Standard Form? Select Three Options.$\[ -5x^2y^4 + 9x^3y^3 + \\]A. \[$x^5\$\]B. \[$y^5\$\]C. \[$-4x^4y^5\$\]D.

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When it comes to creating polynomials in standard form, understanding the rules and conventions is crucial. One of the key aspects is determining the last term of the expression, which can be achieved by selecting the correct option from a given set. In this article, we will explore the process of choosing the last term of a polynomial expression and provide three options to create a polynomial written in standard form.

Understanding Polynomial Expressions

A polynomial expression is a mathematical expression consisting of variables, coefficients, and exponents. It is typically written in the form of a sum of terms, where each term is a product of a coefficient and one or more variables raised to a power. The standard form of a polynomial expression is arranged in descending order of exponents, with the term having the highest exponent first.

The Last Term of a Polynomial Expression

The last term of a polynomial expression is the term that has the lowest exponent. It is the term that is added last when the expression is written in standard form. To create a polynomial written in standard form, we need to select the correct option for the last term.

Option A: x5x^5

Option A is x5x^5. This option would result in a polynomial expression with a single variable, xx, raised to the power of 5. However, this option does not take into account the presence of the variable yy in the original expression. Since the original expression contains both xx and yy, we need to consider an option that includes both variables.

Option B: y5y^5

Option B is y5y^5. This option would result in a polynomial expression with a single variable, yy, raised to the power of 5. Similar to Option A, this option does not take into account the presence of the variable xx in the original expression. We need to consider an option that includes both variables.

Option C: −4x4y5-4x^4y^5

Option C is −4x4y5-4x^4y^5. This option includes both variables, xx and yy, and has a negative coefficient. The exponent of xx is 4, and the exponent of yy is 5, which is consistent with the original expression. This option would result in a polynomial expression with a single term, −4x4y5-4x^4y^5, which is the last term of the expression.

Conclusion

In conclusion, to create a polynomial written in standard form, we need to select the correct option for the last term. Option C, −4x4y5-4x^4y^5, is the correct choice because it includes both variables, xx and yy, and has a negative coefficient. The exponent of xx is 4, and the exponent of yy is 5, which is consistent with the original expression. This option would result in a polynomial expression with a single term, −4x4y5-4x^4y^5, which is the last term of the expression.

Final Answer

In our previous article, we explored the process of creating polynomials in standard form and selecting the correct option for the last term. In this article, we will answer some frequently asked questions related to creating polynomials in standard form.

Q: What is the standard form of a polynomial expression?

A: The standard form of a polynomial expression is arranged in descending order of exponents, with the term having the highest exponent first.

Q: How do I determine the last term of a polynomial expression?

A: To determine the last term of a polynomial expression, you need to select the correct option from a given set. The last term is the term that has the lowest exponent.

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

A: A polynomial expression is a mathematical expression consisting of variables, coefficients, and exponents. A polynomial equation is a mathematical statement that equates a polynomial expression to zero.

Q: Can I have a polynomial expression with only one term?

A: Yes, you can have a polynomial expression with only one term. In this case, the term is the last term of the expression.

Q: How do I write a polynomial expression in standard form?

A: To write a polynomial expression in standard form, you need to arrange the terms in descending order of exponents. You can do this by rearranging the terms in the expression.

Q: What is the importance of writing a polynomial expression in standard form?

A: Writing a polynomial expression in standard form is important because it makes it easier to perform operations such as addition, subtraction, multiplication, and division.

Q: Can I have a polynomial expression with a negative coefficient?

A: Yes, you can have a polynomial expression with a negative coefficient. In this case, the coefficient is a negative number.

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

A: To determine the degree of a polynomial expression, you need to find the highest exponent of any variable in the expression.

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

A: A polynomial expression is a mathematical expression consisting of variables, coefficients, and exponents. A rational expression is a mathematical expression consisting of a fraction of two polynomial expressions.

Q: Can I have a polynomial expression with a variable raised to a negative power?

A: No, you cannot have a polynomial expression with a variable raised to a negative power. In a polynomial expression, the exponent of a variable must be a non-negative integer.

Conclusion

In conclusion, creating polynomials in standard form is an important concept in algebra. By understanding the rules and conventions, you can write polynomial expressions in standard form and perform operations such as addition, subtraction, multiplication, and division. We hope that this article has answered some of your frequently asked questions related to creating polynomials in standard form.

Final Answer

The final answer is that creating polynomials in standard form is an important concept in algebra that requires understanding the rules and conventions. By following the steps outlined in this article, you can write polynomial expressions in standard form and perform operations such as addition, subtraction, multiplication, and division.