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Answer :
To find the difference between the two polynomials [tex]\((21x^4 + 3x^2 - 7)\)[/tex] and [tex]\((-5x^2 + 9x + 8)\)[/tex], we follow these steps:
1. Write down the given expressions:
- First polynomial: [tex]\(21x^4 + 3x^2 - 7\)[/tex].
- Second polynomial: [tex]\(-5x^2 + 9x + 8\)[/tex].
2. Apply the subtraction operation:
We need to subtract the second polynomial from the first:
[tex]\[
(21x^4 + 3x^2 - 7) - (-5x^2 + 9x + 8)
\][/tex]
3. Distribute the negative sign:
When subtracting, distribute the minus sign to each term in the second polynomial:
[tex]\[
21x^4 + 3x^2 - 7 + 5x^2 - 9x - 8
\][/tex]
4. Combine like terms:
- There is only one [tex]\(x^4\)[/tex] term: [tex]\(21x^4\)[/tex].
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(3x^2 + 5x^2 = 8x^2\)[/tex].
- The [tex]\(x\)[/tex] term is: [tex]\(-9x\)[/tex].
- Combine the constant terms: [tex]\(-7 - 8 = -15\)[/tex].
5. Write the final polynomial:
[tex]\[
21x^4 + 8x^2 - 9x - 15
\][/tex]
This result matches the expression given as one of the options. Therefore, the difference of the polynomials is [tex]\(21x^4 + 8x^2 - 9x - 15\)[/tex].
1. Write down the given expressions:
- First polynomial: [tex]\(21x^4 + 3x^2 - 7\)[/tex].
- Second polynomial: [tex]\(-5x^2 + 9x + 8\)[/tex].
2. Apply the subtraction operation:
We need to subtract the second polynomial from the first:
[tex]\[
(21x^4 + 3x^2 - 7) - (-5x^2 + 9x + 8)
\][/tex]
3. Distribute the negative sign:
When subtracting, distribute the minus sign to each term in the second polynomial:
[tex]\[
21x^4 + 3x^2 - 7 + 5x^2 - 9x - 8
\][/tex]
4. Combine like terms:
- There is only one [tex]\(x^4\)[/tex] term: [tex]\(21x^4\)[/tex].
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(3x^2 + 5x^2 = 8x^2\)[/tex].
- The [tex]\(x\)[/tex] term is: [tex]\(-9x\)[/tex].
- Combine the constant terms: [tex]\(-7 - 8 = -15\)[/tex].
5. Write the final polynomial:
[tex]\[
21x^4 + 8x^2 - 9x - 15
\][/tex]
This result matches the expression given as one of the options. Therefore, the difference of the polynomials is [tex]\(21x^4 + 8x^2 - 9x - 15\)[/tex].
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