Question

(7 points)
You are simplifying the following:

(6x3+2x2−5x−14)−(−5x3+7x2+2x−1)
Below is Step 1. Fill in the blanks with the correct sign.

6x3

2x2

5x

14

5x3

7x2

2x

1

Answer 1

To simplify the expression \((6x^3 + 2x^2 - 5x - 14) - (-5x^3 + 7x^2 + 2x - 1)\), we need to distribute the negative sign to all terms in the second set of parentheses. This means changing the signs of each term after the minus sign.

Here's how it looks with the correct signs filled in:

\[
6x^3 \quad + \quad 2x^2 \quad - \quad 5x \quad - \quad 14 \quad + \quad 5x^3 \quad - \quad 7x^2 \quad - \quad 2x \quad + \quad 1
\]

So the completed step with the correct signs would be:

- **6x^3** (no change)
- **+** (the sign remains the same)
- **2x^2** (no change)
- **-** (the sign remains the same)
- **5x** (changed to -5x)
- **-** (the sign remains the same)
- **14** (changed to -14)
- **+** (changed from -5x^3 to +5x^3)
- **-** (changed from +7x^2 to -7x^2)
- **-** (changed from +2x to -2x)
- **+** (changed from -1 to +1)

Now you can proceed to combine like terms.