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Answer :
Certainly! Let's find the difference between the two given polynomials step-by-step.
The problem given is:
[tex]\[
\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right)
\][/tex]
1. Distribute the negative sign across the second polynomial:
[tex]\[
= 5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
When we distribute the minus sign, we change signs of each term in the second polynomial.
2. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- Since there are no other [tex]\(x^3\)[/tex] or constant terms to combine with [tex]\(5x^3\)[/tex] and [tex]\(9\)[/tex], they stay as they are.
- The linear term [tex]\(2x\)[/tex] also remains as there is no other linear term to combine with.
3. Write the result:
[tex]\[
= 5x^3 - 2x^2 + 2x + 9
\][/tex]
So, the difference of the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
This matches one of the options provided: [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
The problem given is:
[tex]\[
\left(5x^3 + 4x^2\right) - \left(6x^2 - 2x - 9\right)
\][/tex]
1. Distribute the negative sign across the second polynomial:
[tex]\[
= 5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
When we distribute the minus sign, we change signs of each term in the second polynomial.
2. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- Since there are no other [tex]\(x^3\)[/tex] or constant terms to combine with [tex]\(5x^3\)[/tex] and [tex]\(9\)[/tex], they stay as they are.
- The linear term [tex]\(2x\)[/tex] also remains as there is no other linear term to combine with.
3. Write the result:
[tex]\[
= 5x^3 - 2x^2 + 2x + 9
\][/tex]
So, the difference of the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
This matches one of the options provided: [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
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