Answer :
To find the difference of the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], we'll follow these steps:
1. Write down the polynomials:
- First polynomial (inside the first set of parentheses): [tex]\(5x^3 + 4x^2\)[/tex]
- Second polynomial (inside the second set of parentheses): [tex]\(6x^2 - 2x - 9\)[/tex]
2. Distribute the negative sign (-) across the second polynomial:
- This means changing the sign of each term in the polynomial. So, [tex]\( (6x^2 - 2x - 9) \)[/tex] becomes [tex]\(-6x^2 + 2x + 9\)[/tex].
3. Subtract the polynomials by combining like terms:
- Combine the terms with the same degree from both polynomials:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
- Group like terms:
- 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]
- Constant terms: [tex]\(9\)[/tex]
4. Write the final result:
- After combining the like terms, we get:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Thus, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
1. Write down the polynomials:
- First polynomial (inside the first set of parentheses): [tex]\(5x^3 + 4x^2\)[/tex]
- Second polynomial (inside the second set of parentheses): [tex]\(6x^2 - 2x - 9\)[/tex]
2. Distribute the negative sign (-) across the second polynomial:
- This means changing the sign of each term in the polynomial. So, [tex]\( (6x^2 - 2x - 9) \)[/tex] becomes [tex]\(-6x^2 + 2x + 9\)[/tex].
3. Subtract the polynomials by combining like terms:
- Combine the terms with the same degree from both polynomials:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
- Group like terms:
- 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]
- Constant terms: [tex]\(9\)[/tex]
4. Write the final result:
- After combining the like terms, we get:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Thus, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
