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Answer :
To find the difference between the two given polynomials, we need to carefully subtract the second polynomial from the first.
Here's how to do it step-by-step:
1. Write down the polynomials being subtracted:
- First polynomial: [tex]\(5x^3 + 4x^2\)[/tex]
- Second polynomial: [tex]\(6x^2 - 2x - 9\)[/tex]
2. Set up the subtraction:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
3. Distribute the minus sign (-) across the second polynomial:
- When distributing the minus sign, the signs of each term in the second polynomial change:
[tex]\[
(5x^3 + 4x^2) - 6x^2 + 2x + 9
\][/tex]
4. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(5x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(0x + 2x = 2x\)[/tex]
- Combine the constant terms: [tex]\(0 + 9 = 9\)[/tex]
5. Write the simplified result:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
This is the difference of the two polynomials after performing the subtraction and simplifying.
Here's how to do it step-by-step:
1. Write down the polynomials being subtracted:
- First polynomial: [tex]\(5x^3 + 4x^2\)[/tex]
- Second polynomial: [tex]\(6x^2 - 2x - 9\)[/tex]
2. Set up the subtraction:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
3. Distribute the minus sign (-) across the second polynomial:
- When distributing the minus sign, the signs of each term in the second polynomial change:
[tex]\[
(5x^3 + 4x^2) - 6x^2 + 2x + 9
\][/tex]
4. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(5x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(0x + 2x = 2x\)[/tex]
- Combine the constant terms: [tex]\(0 + 9 = 9\)[/tex]
5. Write the simplified result:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
This is the difference of the two polynomials after performing the subtraction and simplifying.
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