Answer :
To find the difference of the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], follow these steps:
1. Express the polynomials clearly:
- The first polynomial is [tex]\(5x^3 + 4x^2\)[/tex].
- The second polynomial is [tex]\(6x^2 - 2x - 9\)[/tex].
2. Set up the subtraction:
- The operation is to subtract the second polynomial from the first: [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex].
3. Distribute the negative sign across the second polynomial:
- This changes the expression to: [tex]\(5x^3 + 4x^2 - 6x^2 + 2x + 9\)[/tex].
4. Combine like terms:
- The [tex]\(x^3\)[/tex] terms: [tex]\(5x^3\)[/tex] (there's no [tex]\(x^3\)[/tex] term in the second polynomial to combine with).
- The [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- The [tex]\(x\)[/tex] terms: [tex]\(0x + 2x = 2x\)[/tex].
- The constant terms: [tex]\(0 + 9 = 9\)[/tex].
5. Write the resulting polynomial:
- After combining all like terms, the result is: [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
So, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
1. Express the polynomials clearly:
- The first polynomial is [tex]\(5x^3 + 4x^2\)[/tex].
- The second polynomial is [tex]\(6x^2 - 2x - 9\)[/tex].
2. Set up the subtraction:
- The operation is to subtract the second polynomial from the first: [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex].
3. Distribute the negative sign across the second polynomial:
- This changes the expression to: [tex]\(5x^3 + 4x^2 - 6x^2 + 2x + 9\)[/tex].
4. Combine like terms:
- The [tex]\(x^3\)[/tex] terms: [tex]\(5x^3\)[/tex] (there's no [tex]\(x^3\)[/tex] term in the second polynomial to combine with).
- The [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- The [tex]\(x\)[/tex] terms: [tex]\(0x + 2x = 2x\)[/tex].
- The constant terms: [tex]\(0 + 9 = 9\)[/tex].
5. Write the resulting polynomial:
- After combining all like terms, the result is: [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
So, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
