Answer :
To find the difference of the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], let's perform the subtraction step by step:
1. Write out the polynomials clearly:
- The first polynomial is [tex]\(5x^3 + 4x^2\)[/tex].
- The second polynomial is [tex]\(6x^2 - 2x - 9\)[/tex].
2. Distribute the negative sign across the second polynomial:
- This changes the second polynomial from [tex]\(6x^2 - 2x - 9\)[/tex] to [tex]\(-6x^2 + 2x + 9\)[/tex].
3. Subtract the polynomials by combining like terms:
- [tex]\(5x^3 + 4x^2 - 6x^2 + 2x + 9\)[/tex].
4. Combine like terms:
- The [tex]\(x^3\)[/tex] term is [tex]\(5x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- The [tex]\(x\)[/tex] term is [tex]\(2x\)[/tex].
- The constant term is [tex]\(9\)[/tex].
Therefore, the difference of the polynomials is:
[tex]\[ 5x^3 - 2x^2 + 2x + 9. \][/tex]
The answer is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
1. Write out the polynomials clearly:
- The first polynomial is [tex]\(5x^3 + 4x^2\)[/tex].
- The second polynomial is [tex]\(6x^2 - 2x - 9\)[/tex].
2. Distribute the negative sign across the second polynomial:
- This changes the second polynomial from [tex]\(6x^2 - 2x - 9\)[/tex] to [tex]\(-6x^2 + 2x + 9\)[/tex].
3. Subtract the polynomials by combining like terms:
- [tex]\(5x^3 + 4x^2 - 6x^2 + 2x + 9\)[/tex].
4. Combine like terms:
- The [tex]\(x^3\)[/tex] term is [tex]\(5x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- The [tex]\(x\)[/tex] term is [tex]\(2x\)[/tex].
- The constant term is [tex]\(9\)[/tex].
Therefore, the difference of the polynomials is:
[tex]\[ 5x^3 - 2x^2 + 2x + 9. \][/tex]
The answer is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
