We appreciate your visit to What is the difference of the polynomials tex left 5x 3 4x 2 right left 6x 2 2x 9 right tex A tex x 3. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the difference between the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex] and [tex]\(-x^3 + 6x^2 + 9\)[/tex], we'll proceed step-by-step.
1. Subtract the first two polynomials:
- First Polynomial: [tex]\(5x^3 + 4x^2\)[/tex]
- Second Polynomial: [tex]\(6x^2 - 2x - 9\)[/tex]
We need to subtract the second polynomial from the first, which involves distributing the negative sign and then combining like terms.
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
Combine the like terms:
[tex]\[
5x^3 + (4x^2 - 6x^2) + 2x + 9 = 5x^3 - 2x^2 + 2x + 9
\][/tex]
2. Subtract the third polynomial from the result of the first subtraction:
- Third Polynomial: [tex]\(-x^3 + 6x^2 + 9\)[/tex]
Subtract this polynomial from the result we got in step 1:
[tex]\[
(5x^3 - 2x^2 + 2x + 9) - (-x^3 + 6x^2 + 9)
\][/tex]
Distribute the negative sign and then combine like terms:
[tex]\[
5x^3 - 2x^2 + 2x + 9 + x^3 - 6x^2 - 9
\][/tex]
Combine the like terms:
[tex]\[
(5x^3 + x^3) + (-2x^2 - 6x^2) + 2x + (9 - 9) = 6x^3 - 8x^2 + 2x
\][/tex]
The final result from subtracting the polynomials is [tex]\(6x^3 - 8x^2 + 2x\)[/tex].
So, the difference of the original polynomials is [tex]\(6x^3 - 8x^2 + 2x\)[/tex].
1. Subtract the first two polynomials:
- First Polynomial: [tex]\(5x^3 + 4x^2\)[/tex]
- Second Polynomial: [tex]\(6x^2 - 2x - 9\)[/tex]
We need to subtract the second polynomial from the first, which involves distributing the negative sign and then combining like terms.
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
Combine the like terms:
[tex]\[
5x^3 + (4x^2 - 6x^2) + 2x + 9 = 5x^3 - 2x^2 + 2x + 9
\][/tex]
2. Subtract the third polynomial from the result of the first subtraction:
- Third Polynomial: [tex]\(-x^3 + 6x^2 + 9\)[/tex]
Subtract this polynomial from the result we got in step 1:
[tex]\[
(5x^3 - 2x^2 + 2x + 9) - (-x^3 + 6x^2 + 9)
\][/tex]
Distribute the negative sign and then combine like terms:
[tex]\[
5x^3 - 2x^2 + 2x + 9 + x^3 - 6x^2 - 9
\][/tex]
Combine the like terms:
[tex]\[
(5x^3 + x^3) + (-2x^2 - 6x^2) + 2x + (9 - 9) = 6x^3 - 8x^2 + 2x
\][/tex]
The final result from subtracting the polynomials is [tex]\(6x^3 - 8x^2 + 2x\)[/tex].
So, the difference of the original polynomials is [tex]\(6x^3 - 8x^2 + 2x\)[/tex].
Thanks for taking the time to read What is the difference of the polynomials tex left 5x 3 4x 2 right left 6x 2 2x 9 right tex A tex x 3. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
