Which Expression Can Be Used To Find The Sum Of The Polynomials?A. \[$\left[(9-3x^2) + (-8x^2 + 4x + 5)\right]\$\]B. \[$\left[\left(-3x^2\right) + \left(-8x^2\right)\right] + 4x + \left[9 + (-5)\right]\$\]C. \[$\left[3x^2 +

Introduction

In algebra, polynomials are expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. When dealing with polynomials, it's often necessary to find their sum, which involves combining like terms. In this article, we'll explore the different ways to express the sum of polynomials and identify the correct expression among the given options.

Understanding Polynomials

A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The general form of a polynomial is:

$$a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$$

where $a_n, a_{n-1}, \ldots, a_1, a_0$ are coefficients, and $x$ is the variable.

Like Terms and Combining Polynomials

Like terms are terms that have the same variable raised to the same power. When combining like terms, we add or subtract the coefficients of the like terms. For example:

$$2x^2 + 3x^2 = (2 + 3)x^2 = 5x^2$$

Option A: Correct Expression for Sum of Polynomials

Option A is:

$$\left[(9-3x^2) + (-8x^2 + 4x + 5)\right]$$

To find the sum of the polynomials in Option A, we need to combine like terms:

$$\left[(9-3x^2) + (-8x^2 + 4x + 5)\right]$$

$$= 9 - 3x^2 - 8x^2 + 4x + 5$$

$$= 14 - 11x^2 + 4x$$

Option B: Incorrect Expression for Sum of Polynomials

Option B is:

$$\left[\left(-3x^2\right) + \left(-8x^2\right)\right] + 4x + \left[9 + (-5)\right]$$

To find the sum of the polynomials in Option B, we need to combine like terms:

$$\left[\left(-3x^2\right) + \left(-8x^2\right)\right] + 4x + \left[9 + (-5)\right]$$

$$= -11x^2 + 4x + 4$$

However, this expression is not the correct sum of the polynomials. The correct sum is:

$$14 - 11x^2 + 4x$$

Option C: Incorrect Expression for Sum of Polynomials

Option C is:

$$\left[3x^2 + 9\right] + \left[-8x^2 + 4x + 5\right]$$

To find the sum of the polynomials in Option C, we need to combine like terms:

$$\left[3x^2 + 9\right] + \left[-8x^2 + 4x + 5\right]$$

$$= 3x^2 - 8x^2 + 4x + 9 + 5$$

$$= -5x^2 + 4x + 14$$

However, this expression is not the correct sum of the polynomials. The correct sum is:

$$14 - 11x^2 + 4x$$

Conclusion

In conclusion, the correct expression for finding the sum of the polynomials is Option A:

$$\left[(9-3x^2) + (-8x^2 + 4x + 5)\right]$$

This expression correctly combines like terms to find the sum of the polynomials. Options B and C are incorrect expressions for finding the sum of the polynomials.

Final Answer

The final answer is:

\left[(9-3x^2) + (-8x^2 + 4x + 5)\right]$<br/> **Frequently Asked Questions: Finding the Sum of Polynomials** ===================================================== **Q: What is the general form of a polynomial?** -------------------------------------------- A: The general form of a polynomial is: $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0

where $a_n, a_{n-1}, \ldots, a_1, a_0$ are coefficients, and $x$ is the variable.

Q: What are like terms in polynomials?

A: Like terms are terms that have the same variable raised to the same power. For example:

$$2x^2 + 3x^2 = (2 + 3)x^2 = 5x^2$$

Q: How do I combine like terms in polynomials?

A: To combine like terms, you add or subtract the coefficients of the like terms. For example:

$$2x^2 + 3x^2 = (2 + 3)x^2 = 5x^2$$

$$-2x^2 + 3x^2 = (3 - 2)x^2 = x^2$$

Q: What is the correct expression for finding the sum of the polynomials in Option A?

A: The correct expression for finding the sum of the polynomials in Option A is:

$$\left[(9-3x^2) + (-8x^2 + 4x + 5)\right]$$

This expression correctly combines like terms to find the sum of the polynomials.

Q: What is the correct expression for finding the sum of the polynomials in Option B?

A: The correct expression for finding the sum of the polynomials in Option B is:

$$14 - 11x^2 + 4x$$

This expression correctly combines like terms to find the sum of the polynomials.

Q: What is the correct expression for finding the sum of the polynomials in Option C?

A: The correct expression for finding the sum of the polynomials in Option C is:

$$14 - 11x^2 + 4x$$

This expression correctly combines like terms to find the sum of the polynomials.

Q: How do I determine the correct expression for finding the sum of polynomials?

A: To determine the correct expression for finding the sum of polynomials, you need to combine like terms correctly. This involves adding or subtracting the coefficients of the like terms.

Q: What are some common mistakes to avoid when finding the sum of polynomials?

A: Some common mistakes to avoid when finding the sum of polynomials include:

• Not combining like terms correctly
• Adding or subtracting coefficients incorrectly
• Not simplifying the expression after combining like terms

Q: How can I practice finding the sum of polynomials?

A: You can practice finding the sum of polynomials by working through examples and exercises. You can also use online resources or math software to help you practice.

Conclusion

In conclusion, finding the sum of polynomials involves combining like terms correctly. By following the steps outlined in this article, you can determine the correct expression for finding the sum of polynomials. Remember to practice regularly to build your skills and confidence.

Final Answer

The final answer is:

$$\left[(9-3x^2) + (-8x^2 + 4x + 5)\right]$$