Answer :
To find the difference between the polynomials [tex]\((5x^3 + 4x^2)\)[/tex] and [tex]\((6x^2 - 2x - 9)\)[/tex], follow these steps:
1. Write down the polynomials:
- The first polynomial is [tex]\(5x^3 + 4x^2\)[/tex].
- The second polynomial is [tex]\(6x^2 - 2x - 9\)[/tex].
2. Ensure both polynomials are in standard form:
- For consistency, write both polynomials with all powers of [tex]\(x\)[/tex] up to the highest present power (which is [tex]\(x^3\)[/tex] here) even if some coefficients are zero.
- So, for the first polynomial, it becomes: [tex]\(5x^3 + 4x^2 + 0x + 0\)[/tex].
- For the second polynomial, write it as [tex]\(0x^3 + 6x^2 - 2x - 9\)[/tex].
3. Subtract the second polynomial from the first:
- [tex]\((5x^3 + 4x^2 + 0x + 0) - (0x^3 + 6x^2 - 2x - 9)\)[/tex].
4. Subtract corresponding coefficients:
- For the [tex]\(x^3\)[/tex] term: [tex]\(5 - 0 = 5\)[/tex].
- For the [tex]\(x^2\)[/tex] term: [tex]\(4 - 6 = -2\)[/tex].
- For the [tex]\(x^1\)[/tex] term: [tex]\(0 - (-2) = 2\)[/tex].
- For the constant term: [tex]\(0 - (-9) = 9\)[/tex].
5. Write the resulting polynomial:
- Combine the terms: [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
Therefore, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
1. Write down the polynomials:
- The first polynomial is [tex]\(5x^3 + 4x^2\)[/tex].
- The second polynomial is [tex]\(6x^2 - 2x - 9\)[/tex].
2. Ensure both polynomials are in standard form:
- For consistency, write both polynomials with all powers of [tex]\(x\)[/tex] up to the highest present power (which is [tex]\(x^3\)[/tex] here) even if some coefficients are zero.
- So, for the first polynomial, it becomes: [tex]\(5x^3 + 4x^2 + 0x + 0\)[/tex].
- For the second polynomial, write it as [tex]\(0x^3 + 6x^2 - 2x - 9\)[/tex].
3. Subtract the second polynomial from the first:
- [tex]\((5x^3 + 4x^2 + 0x + 0) - (0x^3 + 6x^2 - 2x - 9)\)[/tex].
4. Subtract corresponding coefficients:
- For the [tex]\(x^3\)[/tex] term: [tex]\(5 - 0 = 5\)[/tex].
- For the [tex]\(x^2\)[/tex] term: [tex]\(4 - 6 = -2\)[/tex].
- For the [tex]\(x^1\)[/tex] term: [tex]\(0 - (-2) = 2\)[/tex].
- For the constant term: [tex]\(0 - (-9) = 9\)[/tex].
5. Write the resulting polynomial:
- Combine the terms: [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
Therefore, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
