Choose The Polynomial That Is Written In Standard Form.A. \[$-3x^5y^2 + 4x^3y + 10x^2\$\]B. \[$-8xy^2 + 4x^4y^2 + 3x^3\$\]C. \[$x^4y^2 + 4x^3y^5 + 10x^4\$\]D. \[$x^6y^2 + 4x^3y^8 + 10x^7\$\]

**Choosing the Correct Polynomial in Standard Form** =====================================================

What is a Polynomial in Standard Form?

A polynomial in standard form is a mathematical expression that consists of variables and coefficients, where the variables are raised to non-negative integer powers. The standard form of a polynomial is typically written with the terms arranged in descending order of the powers of the variables.

How to Identify a Polynomial in Standard Form

To identify a polynomial in standard form, look for the following characteristics:

• The polynomial consists of variables and coefficients.
• The variables are raised to non-negative integer powers.
• The terms are arranged in descending order of the powers of the variables.

Example Polynomials in Standard Form

Here are some examples of polynomials in standard form:

• $2x^3 + 3x^2 - 4x + 1$
• $x^4 + 2x^3 - 3x^2 + x - 1$
• $3x^2 + 2x - 1$

Choosing the Correct Polynomial in Standard Form

Now, let's apply what we've learned to the problem at hand. We are given four options, and we need to choose the one that is written in standard form.

Option A: ${-3x^5y^2 + 4x^3y + 10x^2}$

This polynomial has terms with variables raised to non-negative integer powers. However, the terms are not arranged in descending order of the powers of the variables. Therefore, this is not the correct answer.

Option B: ${-8xy^2 + 4x^4y^2 + 3x^3}$

This polynomial also has terms with variables raised to non-negative integer powers. However, the terms are not arranged in descending order of the powers of the variables. Therefore, this is not the correct answer.

Option C: ${x^4y^2 + 4x^3y^5 + 10x^4}$

This polynomial has terms with variables raised to non-negative integer powers. However, the terms are not arranged in descending order of the powers of the variables. Therefore, this is not the correct answer.

Option D: ${x^6y^2 + 4x^3y^8 + 10x^7}$

This polynomial has terms with variables raised to non-negative integer powers. However, the terms are not arranged in descending order of the powers of the variables. Therefore, this is not the correct answer.

Conclusion

After analyzing all the options, we can conclude that none of the given polynomials are written in standard form. However, if we were to rewrite each polynomial in standard form, we would get:

• Option A: $-3x^5y^2 + 4x^3y + 10x^2$
• Option B: $-8xy^2 + 4x^4y^2 + 3x^3$
• Option C: $x^4y^2 + 4x^3y^5 + 10x^4$
• Option D: $x^6y^2 + 4x^3y^8 + 10x^7$

Q&A

Q: What is a polynomial in standard form? A: A polynomial in standard form is a mathematical expression that consists of variables and coefficients, where the variables are raised to non-negative integer powers.

Q: How do I identify a polynomial in standard form? A: To identify a polynomial in standard form, look for the following characteristics: the polynomial consists of variables and coefficients, the variables are raised to non-negative integer powers, and the terms are arranged in descending order of the powers of the variables.

Q: What are some examples of polynomials in standard form? A: Here are some examples of polynomials in standard form: $2x^3 + 3x^2 - 4x + 1$, $x^4 + 2x^3 - 3x^2 + x - 1$, and $3x^2 + 2x - 1$.

Q: How do I choose the correct polynomial in standard form? A: To choose the correct polynomial in standard form, look for the characteristics mentioned above and arrange the terms in descending order of the powers of the variables.

Q: What is the correct answer among the given options? A: Unfortunately, none of the given options are written in standard form. However, if we were to rewrite each polynomial in standard form, we would get the polynomials mentioned above.

Q: Can you provide more examples of polynomials in standard form? A: Yes, here are some more examples of polynomials in standard form: $x^2 + 3x - 4$, $2x^3 - 5x^2 + 3x + 1$, and $x^4 - 2x^3 + 3x^2 - x + 1$.