Question

1. which of the following is the result of adding the polynomials $x^3 + 2x^2 - x + 1$ and $-x^3 + x^2 + x - 1$?

a. $3x^2$

b. $3x^2 - 2$

c. $-2x^3 + 2x^2 - 2x$

d. $2x^3 - x^2$

Explanation:

Step1: Write the sum expression

$(x^3 + 2x^2 - x + 1) + (-x^3 + x^2 + x - 1)$

Step2: Group like terms

$(x^3 - x^3) + (2x^2 + x^2) + (-x + x) + (1 - 1)$

Step3: Combine like terms

$0x^3 + 3x^2 + 0x + 0 = 3x^2$

Answer:

a. $3x^2$