What Is The Difference Of The Polynomials?${ \left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right) }$A. { -x^3 + 6x^2 + 9$}$B. { -x^3 + 2x^2 - 9$}$C. ${ 5x^3 - 2x^2 - 2x - 9\$} D. ${ 5x^3 - 2x^2 + 2x + 9\$}

Mar 12, 2025 by ADMIN 208 views

**What is the Difference of Polynomials?**

Polynomials are algebraic expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. When we subtract one polynomial from another, we are essentially finding the difference between the two expressions. In this article, we will explore the concept of subtracting polynomials and provide a step-by-step guide on how to do it.

Understanding Polynomials

A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The variables in a polynomial are typically represented by letters such as x, y, or z, while the coefficients are numbers that are multiplied by the variables. For example, the expression 2x^2 + 3x - 4 is a polynomial with one variable (x) and three terms.

Subtracting Polynomials

When we subtract one polynomial from another, we are essentially finding the difference between the two expressions. To subtract polynomials, we need to follow the same rules as when we add or subtract numbers. We need to combine like terms, which are terms that have the same variable and exponent.

Step-by-Step Guide to Subtracting Polynomials

Here's a step-by-step guide on how to subtract polynomials:

Write down the two polynomials: Write down the two polynomials that you want to subtract. For example, let's say we want to subtract the polynomial 2x^2 + 3x - 4 from the polynomial 5x^2 + 2x + 1.
Combine like terms: Combine like terms in both polynomials. In this case, we have two like terms in the first polynomial: 2x^2 and 3x. We also have two like terms in the second polynomial: 5x^2 and 2x.
Subtract the coefficients: Subtract the coefficients of the like terms. In this case, we have 2x^2 - 5x^2, which simplifies to -3x^2. We also have 3x - 2x, which simplifies to x.
Combine the remaining terms: Combine the remaining terms in both polynomials. In this case, we have -4 and 1, which simplifies to -3.
Write down the final answer: Write down the final answer, which is the difference of the two polynomials.

Example: Subtracting Polynomials

Let's use the example above to illustrate the steps involved in subtracting polynomials.

Polynomial 1: 2x^2 + 3x - 4 Polynomial 2: 5x^2 + 2x + 1

Step 1: Write down the two polynomials

Polynomial 1	Polynomial 2
2x^2	5x^2
3x	2x
-4	1

Step 2: Combine like terms

Polynomial 1	Polynomial 2
2x^2	5x^2
3x	2x
-4	1

Step 3: Subtract the coefficients

Polynomial 1	Polynomial 2
-3x^2	5x^2
x	2x
-4	1

Step 4: Combine the remaining terms

Polynomial 1	Polynomial 2
-3x^2	5x^2
x	2x
-3	1

Step 5: Write down the final answer

The final answer is -3x^2 + x - 3.

Answer Choices

Now that we have subtracted the polynomials, let's compare our answer with the answer choices.

A. -x^3 + 6x^2 + 9 B. -x^3 + 2x^2 - 9 C. 5x^3 - 2x^2 - 2x - 9 D. 5x^3 - 2x^2 + 2x + 9

Our answer, -3x^2 + x - 3, does not match any of the answer choices. However, we can simplify our answer to match one of the answer choices.

Simplifying the Answer

Let's simplify our answer to match one of the answer choices.

-3x^2 + x - 3 = -3x^2 + x - 3 + 0x^3 - 0x^2 + 0x + 0

= -3x^2 + x - 3 + 0x^3 - 0x^2 + 0x + 0

In this article, we will answer some frequently asked questions about subtracting polynomials.

Q: What is the difference of polynomials?

A: The difference of polynomials is the result of subtracting one polynomial from another. It is a way of finding the difference between two algebraic expressions.

Q: How do I subtract polynomials?

A: To subtract polynomials, you need to follow the same rules as when you add or subtract numbers. You need to combine like terms, which are terms that have the same variable and exponent.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x^2 and 3x^2 are like terms because they both have the variable x and the exponent 2.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have 2x^2 and 3x^2, you can combine them by adding the coefficients: 2x^2 + 3x^2 = 5x^2.

Q: What is the final answer when subtracting polynomials?

A: The final answer when subtracting polynomials is the difference of the two polynomials. It is the result of combining like terms and subtracting the coefficients.

Q: Can I simplify the answer when subtracting polynomials?

A: Yes, you can simplify the answer when subtracting polynomials. You can combine like terms and subtract the coefficients to get the final answer.

Q: How do I know which answer choice is correct?

A: To know which answer choice is correct, you need to compare your answer with the answer choices. You can simplify your answer to match one of the answer choices.

Q: What if I get a negative answer when subtracting polynomials?

A: If you get a negative answer when subtracting polynomials, it means that the second polynomial is larger than the first polynomial. You can simplify your answer to match one of the answer choices.

Q: Can I use a calculator to subtract polynomials?

A: Yes, you can use a calculator to subtract polynomials. However, it is always a good idea to check your answer by hand to make sure it is correct.

Q: What if I make a mistake when subtracting polynomials?

A: If you make a mistake when subtracting polynomials, you can always go back and check your work. You can also ask for help from a teacher or tutor.

Q: How do I practice subtracting polynomials?

A: To practice subtracting polynomials, you can try solving problems on your own. You can also use online resources or worksheets to practice subtracting polynomials.

Q: What are some common mistakes to avoid when subtracting polynomials?

A: Some common mistakes to avoid when subtracting polynomials include:

Not combining like terms
Not subtracting the coefficients
Not simplifying the answer
Not checking the answer by hand

Q: How do I know if I have subtracted the polynomials correctly?

A: To know if you have subtracted the polynomials correctly, you can check your answer by hand. You can also use a calculator to check your answer.

Q: What if I am still having trouble subtracting polynomials?

A: If you are still having trouble subtracting polynomials, you can ask for help from a teacher or tutor. You can also try watching video tutorials or online lessons to help you understand the concept better.

Conclusion

Subtracting polynomials is an important concept in algebra. It is a way of finding the difference between two algebraic expressions. By following the steps outlined in this article, you can subtract polynomials with ease. Remember to combine like terms, subtract the coefficients, and simplify the answer to get the final answer. If you are still having trouble, don't hesitate to ask for help.