Answer :
To find the difference of the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], follow these steps:
1. Identify the Polynomials:
- The first polynomial is [tex]\(5x^3 + 4x^2\)[/tex].
- The second polynomial is [tex]\(6x^2 - 2x - 9\)[/tex].
2. Subtract the Polynomials:
- When subtracting polynomials, distribute the negative sign across the second polynomial:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
3. Combine Like Terms:
- Group the terms with the same degree:
- The [tex]\(x^3\)[/tex] terms: [tex]\(5x^3\)[/tex].
- The [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- The [tex]\(x\)[/tex] terms: [tex]\(2x\)[/tex].
- The constant terms: [tex]\(9\)[/tex].
4. Write the Simplified Expression:
- Combine the terms: [tex]\(5x^3\)[/tex], [tex]\(-2x^2\)[/tex], [tex]\(2x\)[/tex], and [tex]\(9\)[/tex].
- This gives the final expression:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Therefore, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
1. Identify the Polynomials:
- The first polynomial is [tex]\(5x^3 + 4x^2\)[/tex].
- The second polynomial is [tex]\(6x^2 - 2x - 9\)[/tex].
2. Subtract the Polynomials:
- When subtracting polynomials, distribute the negative sign across the second polynomial:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
3. Combine Like Terms:
- Group the terms with the same degree:
- The [tex]\(x^3\)[/tex] terms: [tex]\(5x^3\)[/tex].
- The [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- The [tex]\(x\)[/tex] terms: [tex]\(2x\)[/tex].
- The constant terms: [tex]\(9\)[/tex].
4. Write the Simplified Expression:
- Combine the terms: [tex]\(5x^3\)[/tex], [tex]\(-2x^2\)[/tex], [tex]\(2x\)[/tex], and [tex]\(9\)[/tex].
- This gives the final expression:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Therefore, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
