The problem asks us to add three polynomials: $(x^2 + 8x - 7) + (-4x^2 - 2x + 1) + (x^2 - x - 2)$. We need to simplify the result and avoid factoring.

1. Problem Description

The problem asks us to add three polynomials: $(x^2 + 8x - 7) + (-4x^2 - 2x + 1) + (x^2 - x - 2)$. We need to simplify the result and avoid factoring.

2. Solution Steps

First, we write out the sum of the polynomials:

$(x^2 + 8x - 7) + (-4x^2 - 2x + 1) + (x^2 - x - 2)$

Next, we combine like terms. We group the $x^2$ terms, the $x$ terms, and the constant terms:

$(x^2 - 4x^2 + x^2) + (8x - 2x - x) + (-7 + 1 - 2)$

Now, we simplify each group of terms:

$x^2 - 4x^2 + x^2 = (1 - 4 + 1)x^2 = -2x^2$

$8x - 2x - x = (8 - 2 - 1)x = 5x$

$-7 + 1 - 2 = -6 - 2 = -8$

So the simplified polynomial is:

$-2x^2 + 5x - 8$

3. Final Answer

$-2x^2 + 5x - 8$