Subtract These Polynomials:$\[ \left(3x^2 + 3x + 3\right) - \left(x^2 + 2x + 3\right) \\]A. \[$2x^2 + 5x\$\]B. \[$2x^2 + X\$\]C. \[$2x^2 + X + 6\$\]D. \[$2x^2 + 5x + 6\$\]

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Introduction

Polynomials are algebraic expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. In this article, we will focus on subtracting polynomials, which is an essential operation in algebra. We will use the given problem as an example to demonstrate the step-by-step process of subtracting polynomials.

The Problem

The problem requires us to subtract the polynomial (x2+2x+3)\left(x^2 + 2x + 3\right) from (3x2+3x+3)\left(3x^2 + 3x + 3\right). To do this, we need to follow the rules of subtracting polynomials.

Subtracting Polynomials

When subtracting polynomials, we need to subtract each term of the second polynomial from the corresponding term of the first polynomial. This means that we need to subtract the coefficients of the same degree of the two polynomials.

Step 1: Subtract the Coefficients of the Same Degree

To subtract the polynomials, we need to subtract the coefficients of the same degree. In this case, we have:

  • 3x23x^2 (from the first polynomial) - x2x^2 (from the second polynomial) = 2x22x^2
  • 3x3x (from the first polynomial) - 2x2x (from the second polynomial) = xx
  • 33 (from the first polynomial) - 33 (from the second polynomial) = 00

Step 2: Write the Resulting Polynomial

Now that we have subtracted the coefficients of the same degree, we can write the resulting polynomial. The resulting polynomial is:

2x2+x2x^2 + x

Conclusion

In this article, we have demonstrated the step-by-step process of subtracting polynomials. We used the given problem as an example to show how to subtract the coefficients of the same degree and write the resulting polynomial. The resulting polynomial is 2x2+x2x^2 + x.

Answer

The correct answer is:

  • B. 2x2+x2x^2 + x

Discussion

Subtracting polynomials is an essential operation in algebra. It is used to simplify expressions and solve equations. In this article, we have demonstrated the step-by-step process of subtracting polynomials. We hope that this article has provided a clear understanding of how to subtract polynomials.

Example Problems

Here are some example problems to practice subtracting polynomials:

  • Subtract the polynomial (2x2+4x+1)\left(2x^2 + 4x + 1\right) from (x2+3x+2)\left(x^2 + 3x + 2\right).
  • Subtract the polynomial (3x2+2x+1)\left(3x^2 + 2x + 1\right) from (2x2+4x+3)\left(2x^2 + 4x + 3\right).
  • Subtract the polynomial (x2+2x+1)\left(x^2 + 2x + 1\right) from (3x2+4x+2)\left(3x^2 + 4x + 2\right).

Tips and Tricks

Here are some tips and tricks to help you subtract polynomials:

  • Make sure to subtract the coefficients of the same degree.
  • Use the distributive property to simplify the expression.
  • Check your work by adding the two polynomials together.

Conclusion

In conclusion, subtracting polynomials is an essential operation in algebra. It is used to simplify expressions and solve equations. In this article, we have demonstrated the step-by-step process of subtracting polynomials. We hope that this article has provided a clear understanding of how to subtract polynomials.

Final Answer

The final answer is:

  • B. 2x2+x2x^2 + x

Note: The final answer is the same as the answer provided in the discussion section. This is because the problem is a simple subtraction of polynomials, and the resulting polynomial is 2x2+x2x^2 + x.

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Introduction

Subtracting polynomials is an essential operation in algebra. In this article, we will answer some frequently asked questions (FAQs) on subtracting polynomials. We will cover topics such as the rules of subtracting polynomials, how to subtract polynomials with different degrees, and how to simplify expressions.

Q&A

Q: What are the rules of subtracting polynomials?

A: The rules of subtracting polynomials are as follows:

  • Subtract the coefficients of the same degree.
  • Use the distributive property to simplify the expression.
  • Check your work by adding the two polynomials together.

Q: How do I subtract polynomials with different degrees?

A: To subtract polynomials with different degrees, you need to follow the rules of subtracting polynomials. For example, if you have the polynomials x2+2x+1x^2 + 2x + 1 and 3x2+4x+23x^2 + 4x + 2, you would subtract the coefficients of the same degree:

  • 3x23x^2 (from the second polynomial) - x2x^2 (from the first polynomial) = 2x22x^2
  • 4x4x (from the second polynomial) - 2x2x (from the first polynomial) = 2x2x
  • 22 (from the second polynomial) - 11 (from the first polynomial) = 11

The resulting polynomial is 2x2+2x+12x^2 + 2x + 1.

Q: How do I simplify expressions when subtracting polynomials?

A: To simplify expressions when subtracting polynomials, you need to use the distributive property. For example, if you have the polynomials x2+2x+1x^2 + 2x + 1 and 3x2+4x+23x^2 + 4x + 2, you would simplify the expression by combining like terms:

  • x2+2x+1x^2 + 2x + 1 - 3x2+4x+23x^2 + 4x + 2 = βˆ’2x2βˆ’2xβˆ’1-2x^2 - 2x - 1

The resulting polynomial is βˆ’2x2βˆ’2xβˆ’1-2x^2 - 2x - 1.

Q: What is the difference between subtracting polynomials and adding polynomials?

A: The difference between subtracting polynomials and adding polynomials is the sign of the coefficients. When subtracting polynomials, you need to change the sign of the coefficients of the second polynomial. For example, if you have the polynomials x2+2x+1x^2 + 2x + 1 and 3x2+4x+23x^2 + 4x + 2, you would subtract the coefficients of the same degree:

  • 3x23x^2 (from the second polynomial) - x2x^2 (from the first polynomial) = 2x22x^2
  • 4x4x (from the second polynomial) - 2x2x (from the first polynomial) = 2x2x
  • 22 (from the second polynomial) - 11 (from the first polynomial) = 11

The resulting polynomial is 2x2+2x+12x^2 + 2x + 1.

Q: Can I subtract polynomials with variables of different degrees?

A: Yes, you can subtract polynomials with variables of different degrees. For example, if you have the polynomials x2+2x+1x^2 + 2x + 1 and 3x3+4x+23x^3 + 4x + 2, you would subtract the coefficients of the same degree:

  • 3x33x^3 (from the second polynomial) - x2x^2 (from the first polynomial) = 3x3βˆ’x23x^3 - x^2
  • 4x4x (from the second polynomial) - 2x2x (from the first polynomial) = 2x2x
  • 22 (from the second polynomial) - 11 (from the first polynomial) = 11

The resulting polynomial is 3x3βˆ’x2+2x+13x^3 - x^2 + 2x + 1.

Conclusion

In conclusion, subtracting polynomials is an essential operation in algebra. In this article, we have answered some frequently asked questions (FAQs) on subtracting polynomials. We hope that this article has provided a clear understanding of how to subtract polynomials and simplify expressions.

Final Answer

The final answer is:

  • Yes, you can subtract polynomials with variables of different degrees.

Note: The final answer is the same as the answer provided in the Q&A section. This is because the question is asking if it is possible to subtract polynomials with variables of different degrees, and the answer is yes.