Which Terms Could Be Used As The First Term Of The Expression Below To Create A Polynomial Written In Standard Form? Select Five Options.${ +8r 2s 4 - 3r 3s 3 }$A. { \frac{55^7}{6}$}$B. { S^5$}$C. ${ 34^4 5\$} D.

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Introduction to Polynomial Expressions

A polynomial expression is a mathematical expression that consists of variables and coefficients combined using only addition, subtraction, and multiplication. In a polynomial expression, the variables are raised to non-negative integer powers, and the coefficients are real numbers. The standard form of a polynomial expression is a way of writing the expression with the terms arranged in a specific order.

Standard Form of a Polynomial Expression

The standard form of a polynomial expression is a way of writing the expression with the terms arranged in descending order of the powers of the variables. For example, the polynomial expression 3x2+2x−43x^2 + 2x - 4 is in standard form because the terms are arranged in descending order of the powers of the variable xx.

Selecting the First Term of a Polynomial Expression

When creating a polynomial expression in standard form, we need to select the first term of the expression. The first term is the term with the highest power of the variable. In the given expression +8r2s4−3r3s3+8r^2s^4 - 3r^3s^3, the first term is 8r2s48r^2s^4.

Options for the First Term of the Expression

We are given five options for the first term of the expression:

Option A: 5576\frac{55^7}{6}

This option is not a suitable choice for the first term of the expression because it does not contain the variables rr and ss. The first term of the expression must contain the variables rr and ss.

Option B: s5s^5

This option is not a suitable choice for the first term of the expression because it does not contain the variable rr. The first term of the expression must contain both the variables rr and ss.

Option C: 344534^4 5

This option is not a suitable choice for the first term of the expression because it does not contain the variables rr and ss. The first term of the expression must contain the variables rr and ss.

Option D: r2s4r^2s^4

This option is a suitable choice for the first term of the expression because it contains both the variables rr and ss. The term r2s4r^2s^4 has a power of 2 for the variable rr and a power of 4 for the variable ss.

Option E: −3r3s3-3r^3s^3

This option is a suitable choice for the first term of the expression because it contains both the variables rr and ss. The term −3r3s3-3r^3s^3 has a power of 3 for the variable rr and a power of 3 for the variable ss.

Conclusion

In conclusion, the options for the first term of the expression are r2s4r^2s^4 and −3r3s3-3r^3s^3. These options are suitable choices for the first term of the expression because they contain both the variables rr and ss.

Final Answer

The final answer is: r2s4,−3r3s3\boxed{r^2s^4, -3r^3s^3}

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Introduction to Polynomial Expressions in Standard Form

In our previous article, we discussed the concept of polynomial expressions in standard form. We also explored the options for the first term of a polynomial expression. In this article, we will answer some frequently asked questions about polynomial expressions in standard form.

Q: What is a polynomial expression?

A polynomial expression is a mathematical expression that consists of variables and coefficients combined using only addition, subtraction, and multiplication. In a polynomial expression, the variables are raised to non-negative integer powers, and the coefficients are real numbers.

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

The standard form of a polynomial expression is a way of writing the expression with the terms arranged in a specific order. The terms are arranged in descending order of the powers of the variables.

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

To determine the first term of a polynomial expression, you need to identify the term with the highest power of the variable. In the given expression +8r2s4−3r3s3+8r^2s^4 - 3r^3s^3, the first term is 8r2s48r^2s^4.

Q: What are some common mistakes to avoid when writing a polynomial expression in standard form?

Some common mistakes to avoid when writing a polynomial expression in standard form include:

  • Not arranging the terms in descending order of the powers of the variables
  • Not including all the terms in the expression
  • Not using the correct notation for the variables and coefficients

Q: How do I simplify a polynomial expression?

To simplify a polynomial expression, you need to combine like terms. Like terms are terms that have the same variable and power. For example, in the expression 3x2+2x+4x23x^2 + 2x + 4x^2, the like terms are 3x23x^2 and 4x24x^2. You can combine these terms by adding their coefficients: 3x2+4x2=7x23x^2 + 4x^2 = 7x^2.

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

A polynomial expression is a type of algebraic expression that consists of variables and coefficients combined using only addition, subtraction, and multiplication. An algebraic expression, on the other hand, can include any combination of variables, coefficients, and mathematical operations.

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

No, a polynomial expression cannot have a variable raised to a negative power. In a polynomial expression, the variables are raised to non-negative integer powers.

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

No, a polynomial expression cannot have a variable raised to a fractional power. In a polynomial expression, the variables are raised to non-negative integer powers.

Q: Can I have a polynomial expression with a variable raised to a power that is not an integer?

No, a polynomial expression cannot have a variable raised to a power that is not an integer. In a polynomial expression, the variables are raised to non-negative integer powers.

Conclusion

In conclusion, polynomial expressions in standard form are an important concept in mathematics. By understanding the rules and conventions for writing polynomial expressions in standard form, you can simplify complex expressions and solve problems more efficiently.

Final Answer

The final answer is: There is no final numerical answer to this article. The article is a Q&A about polynomial expressions in standard form.