Question

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

(5x3 +x^2−x) + (8x^2+3x + 1)


(1 point)

Answer 1

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

1. **Arrange the terms**:
- The first polynomial: \( 5x^3 + x^2 - x \)
- The second polynomial: \( 8x^2 + 3x + 1 \)

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

3. **Write the result in standard form**:
\[
5x^3 + 9x^2 + 2x + 1
\]

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