Question

Add. Express your answer as a polynomial in standard form:

(5x3 +x2−x) + (8x2+3x + 1)

(1 point)
Responses

13x3+ 4x2−x − 1
13x3+ 4x2−x − 1

5x3+9x2+2x + 1
5x3+9x2+2x + 1

5x3+8x2−2x + 1
5x3+8x2−2x + 1

None of the above

Answer 1

To add the polynomials \( (5x^3 + x^2 - x) + (8x^2 + 3x + 1) \), we will combine like terms.

1. Start with the first polynomial:
\[
5x^3 + x^2 - x
\]

2. Now add the second polynomial:
\[
+ (8x^2 + 3x + 1)
\]

3. Combine the like terms:
- For \( x^3 \): \( 5x^3 \)
- For \( x^2 \): \( x^2 + 8x^2 = 9x^2 \)
- For \( x \): \( -x + 3x = 2x \)
- For the constant term: \( 1 \)

Putting it all together, we have:
\[
5x^3 + 9x^2 + 2x + 1
\]

Thus, the final answer in standard form is:
\[
\boxed{5x^3 + 9x^2 + 2x + 1}
\]

This matches the second response option:
**5x^3 + 9x^2 + 2x + 1**.