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 Expression for Subtraction:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
2. Distribute the Negative Sign:
When subtracting, distribute the negative sign to each term in the second polynomial:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
Notice that subtracting a negative [tex]\(-(-9)\)[/tex] becomes positive (+9).
3. Combine Like Terms:
- Identify and combine like terms (terms with the same power of [tex]\(x\)[/tex]):
For [tex]\(x^3\)[/tex]: There is only one term: [tex]\(5x^3\)[/tex].
For [tex]\(x^2\)[/tex]: Combine [tex]\(4x^2 - 6x^2\)[/tex], which equals [tex]\(-2x^2\)[/tex].
For [tex]\(x\)[/tex]: There's only one term: [tex]\(+2x\)[/tex].
Constant terms: The only constant term is [tex]\(+9\)[/tex].
4. Write the Combined Result:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Therefore, the difference between the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
1. Write Down the Expression for Subtraction:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
2. Distribute the Negative Sign:
When subtracting, distribute the negative sign to each term in the second polynomial:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
Notice that subtracting a negative [tex]\(-(-9)\)[/tex] becomes positive (+9).
3. Combine Like Terms:
- Identify and combine like terms (terms with the same power of [tex]\(x\)[/tex]):
For [tex]\(x^3\)[/tex]: There is only one term: [tex]\(5x^3\)[/tex].
For [tex]\(x^2\)[/tex]: Combine [tex]\(4x^2 - 6x^2\)[/tex], which equals [tex]\(-2x^2\)[/tex].
For [tex]\(x\)[/tex]: There's only one term: [tex]\(+2x\)[/tex].
Constant terms: The only constant term is [tex]\(+9\)[/tex].
4. Write the Combined Result:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Therefore, the difference between the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
