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Answer :
To find the difference of the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], we can break it down into simple steps.
1. Write down the polynomials:
- The first polynomial is [tex]\(5x^3 + 4x^2\)[/tex].
- The second polynomial to subtract is [tex]\(6x^2 - 2x - 9\)[/tex].
2. Distribute the negative sign:
When subtracting, you need to distribute the negative sign across the entire second polynomial:
[tex]\(-(6x^2 - 2x - 9) = -6x^2 + 2x + 9\)[/tex].
3. Combine the polynomials:
Now, you add the result from step 2 to the first polynomial:
[tex]\[
(5x^3 + 4x^2) + (-6x^2 + 2x + 9).
\][/tex]
4. Combine like terms:
- For the [tex]\(x^3\)[/tex] terms: there is only [tex]\(5x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- For the [tex]\(x\)[/tex] terms: there is only [tex]\(2x\)[/tex].
- For the constant terms: [tex]\(9\)[/tex].
5. Write the final result:
So, the result after combining the like terms is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
This is the difference of the polynomials.
1. Write down the polynomials:
- The first polynomial is [tex]\(5x^3 + 4x^2\)[/tex].
- The second polynomial to subtract is [tex]\(6x^2 - 2x - 9\)[/tex].
2. Distribute the negative sign:
When subtracting, you need to distribute the negative sign across the entire second polynomial:
[tex]\(-(6x^2 - 2x - 9) = -6x^2 + 2x + 9\)[/tex].
3. Combine the polynomials:
Now, you add the result from step 2 to the first polynomial:
[tex]\[
(5x^3 + 4x^2) + (-6x^2 + 2x + 9).
\][/tex]
4. Combine like terms:
- For the [tex]\(x^3\)[/tex] terms: there is only [tex]\(5x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- For the [tex]\(x\)[/tex] terms: there is only [tex]\(2x\)[/tex].
- For the constant terms: [tex]\(9\)[/tex].
5. Write the final result:
So, the result after combining the like terms is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
This is the difference of the polynomials.
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