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

Question

(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: \[ \boxed{5x^3 + 9x^2 + 2x + 1} \]