College

Perform the operation:

\[ (3x^3 - 7x^2 + 5x - 2) + (2x^2 - 9x + 8) \]

A. \[ 3x^3 - 9x^2 + 14x - 10 \]

B. \[ 3x^3 - 5x^2 - 4x + 6 \]

C. \[ 5x^5 - 16x^3 + 13x - 2 \]

D. \[ -14x^4 + 3x^3 - 45x^2 - 16 \]

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].