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Answer :
To perform the operation of adding the two polynomials [tex]\((3x^3 - 7x^2 + 5x - 2)\)[/tex] and [tex]\((2x^2 - 9x + 8)\)[/tex], follow these steps:
1. Align the Like Terms: Make sure to write the polynomials in an organized way, aligning like terms (terms with the same power of [tex]\(x\)[/tex]).
- The first polynomial is: [tex]\(3x^3 - 7x^2 + 5x - 2\)[/tex].
- The second polynomial can be thought of as: [tex]\(0x^3 + 2x^2 - 9x + 8\)[/tex].
2. Add the Coefficients of Like Terms:
- [tex]\(x^3\)[/tex] Terms: There is only one term, [tex]\(3x^3\)[/tex], so it remains the same: [tex]\(3x^3\)[/tex].
- [tex]\(x^2\)[/tex] Terms: Combine [tex]\(-7x^2\)[/tex] and [tex]\(2x^2\)[/tex]:
[tex]\[
-7 + 2 = -5, \quad \text{so the result is } -5x^2.
\][/tex]
- [tex]\(x\)[/tex] Terms: Combine [tex]\(5x\)[/tex] and [tex]\(-9x\)[/tex]:
[tex]\[
5 + (-9) = -4, \quad \text{so the result is } -4x.
\][/tex]
- Constant Terms: Combine [tex]\(-2\)[/tex] and [tex]\(8\)[/tex]:
[tex]\[
-2 + 8 = 6.
\][/tex]
3. Write the Result: Combine the results from each step above to form the resulting polynomial:
[tex]\[
3x^3 - 5x^2 - 4x + 6
\][/tex]
Thus, the result of adding the two polynomials is [tex]\(3x^3 - 5x^2 - 4x + 6\)[/tex].
1. Align the Like Terms: Make sure to write the polynomials in an organized way, aligning like terms (terms with the same power of [tex]\(x\)[/tex]).
- The first polynomial is: [tex]\(3x^3 - 7x^2 + 5x - 2\)[/tex].
- The second polynomial can be thought of as: [tex]\(0x^3 + 2x^2 - 9x + 8\)[/tex].
2. Add the Coefficients of Like Terms:
- [tex]\(x^3\)[/tex] Terms: There is only one term, [tex]\(3x^3\)[/tex], so it remains the same: [tex]\(3x^3\)[/tex].
- [tex]\(x^2\)[/tex] Terms: Combine [tex]\(-7x^2\)[/tex] and [tex]\(2x^2\)[/tex]:
[tex]\[
-7 + 2 = -5, \quad \text{so the result is } -5x^2.
\][/tex]
- [tex]\(x\)[/tex] Terms: Combine [tex]\(5x\)[/tex] and [tex]\(-9x\)[/tex]:
[tex]\[
5 + (-9) = -4, \quad \text{so the result is } -4x.
\][/tex]
- Constant Terms: Combine [tex]\(-2\)[/tex] and [tex]\(8\)[/tex]:
[tex]\[
-2 + 8 = 6.
\][/tex]
3. Write the Result: Combine the results from each step above to form the resulting polynomial:
[tex]\[
3x^3 - 5x^2 - 4x + 6
\][/tex]
Thus, the result of adding the two polynomials is [tex]\(3x^3 - 5x^2 - 4x + 6\)[/tex].
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