Answer :
To find the difference between the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], let's go through the steps:
1. Rewrite the expression: Begin by writing the polynomial expression fully, which is:
[tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex].
2. Distribute the negative sign: Distribute the negative sign across the second polynomial:
[tex]\((5x^3 + 4x^2) - 6x^2 + 2x + 9\)[/tex].
3. Combine like terms: Now bring together the like terms:
- The terms involving [tex]\(x^3\)[/tex]: [tex]\(5x^3\)[/tex]
- The terms involving [tex]\(x^2\)[/tex]: [tex]\(4x^2 - 6x^2\)[/tex]
- The terms involving [tex]\(x\)[/tex]: [tex]\(2x\)[/tex]
- Constant terms: [tex]\(9\)[/tex]
4. Perform the subtraction for each term:
- [tex]\(x^3\)[/tex] term: [tex]\(5x^3\)[/tex] (only one term)
- [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- [tex]\(x\)[/tex] term: [tex]\(2x\)[/tex] (only one term)
- Constant terms: [tex]\(9\)[/tex] (only one constant)
5. Write down the resulting polynomial:
The difference is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
Therefore, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
1. Rewrite the expression: Begin by writing the polynomial expression fully, which is:
[tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex].
2. Distribute the negative sign: Distribute the negative sign across the second polynomial:
[tex]\((5x^3 + 4x^2) - 6x^2 + 2x + 9\)[/tex].
3. Combine like terms: Now bring together the like terms:
- The terms involving [tex]\(x^3\)[/tex]: [tex]\(5x^3\)[/tex]
- The terms involving [tex]\(x^2\)[/tex]: [tex]\(4x^2 - 6x^2\)[/tex]
- The terms involving [tex]\(x\)[/tex]: [tex]\(2x\)[/tex]
- Constant terms: [tex]\(9\)[/tex]
4. Perform the subtraction for each term:
- [tex]\(x^3\)[/tex] term: [tex]\(5x^3\)[/tex] (only one term)
- [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- [tex]\(x\)[/tex] term: [tex]\(2x\)[/tex] (only one term)
- Constant terms: [tex]\(9\)[/tex] (only one constant)
5. Write down the resulting polynomial:
The difference is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
Therefore, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
