Answer :
Sure! Let's solve this step-by-step.
We are tasked with finding the difference between two polynomials:
[tex]\[
(x^4 + x^3 + x^2 + x) - (x^4 - x^3 + x^2 - x)
\][/tex]
Let's break it down:
1. Distribute the negative sign in the second polynomial:
[tex]\[
-(x^4 - x^3 + x^2 - x) = -x^4 + x^3 - x^2 + x
\][/tex]
2. Combine the polynomials by subtracting each term:
[tex]\[
(x^4 + x^3 + x^2 + x) + (-x^4 + x^3 - x^2 + x)
\][/tex]
3. Perform the subtraction:
- For the [tex]\(x^4\)[/tex] terms: [tex]\(x^4 - x^4 = 0\)[/tex]
- For the [tex]\(x^3\)[/tex] terms: [tex]\(x^3 + x^3 = 2x^3\)[/tex]
- For the [tex]\(x^2\)[/tex] terms: [tex]\(x^2 - x^2 = 0\)[/tex]
- For the [tex]\(x\)[/tex] terms: [tex]\(x + x = 2x\)[/tex]
4. Combine the simplified terms:
[tex]\[
2x^3 + 2x
\][/tex]
So, the difference of the polynomials is [tex]\(2x^3 + 2x\)[/tex]. Unfortunately, this does not match the given answer choices, so make sure everything was correct in the problem setup, as there might be a discrepancy.
We are tasked with finding the difference between two polynomials:
[tex]\[
(x^4 + x^3 + x^2 + x) - (x^4 - x^3 + x^2 - x)
\][/tex]
Let's break it down:
1. Distribute the negative sign in the second polynomial:
[tex]\[
-(x^4 - x^3 + x^2 - x) = -x^4 + x^3 - x^2 + x
\][/tex]
2. Combine the polynomials by subtracting each term:
[tex]\[
(x^4 + x^3 + x^2 + x) + (-x^4 + x^3 - x^2 + x)
\][/tex]
3. Perform the subtraction:
- For the [tex]\(x^4\)[/tex] terms: [tex]\(x^4 - x^4 = 0\)[/tex]
- For the [tex]\(x^3\)[/tex] terms: [tex]\(x^3 + x^3 = 2x^3\)[/tex]
- For the [tex]\(x^2\)[/tex] terms: [tex]\(x^2 - x^2 = 0\)[/tex]
- For the [tex]\(x\)[/tex] terms: [tex]\(x + x = 2x\)[/tex]
4. Combine the simplified terms:
[tex]\[
2x^3 + 2x
\][/tex]
So, the difference of the polynomials is [tex]\(2x^3 + 2x\)[/tex]. Unfortunately, this does not match the given answer choices, so make sure everything was correct in the problem setup, as there might be a discrepancy.
