Question

2. Use addition and subtraction to simplify the following polynomials.
A. Add polynomials: (3 – 4x + 8x2) + (–6 + 2x – 5x2)
Step 1: Rewrite the polynomials without the parentheses.

-3 -2x +3x2


3 -4x + 8x2- 6 + 2x – 5x2


3 -4x + 8x2+ 6 + 2x – 5x2


9 -2x + 8x2 – 5x2

Answer 1

To add the polynomials \((3 - 4x + 8x^2) + (-6 + 2x - 5x^2)\), we can follow these steps:

### Step 1: Rewrite the polynomials without the parentheses.

The expression becomes:
\[
3 - 4x + 8x^2 - 6 + 2x - 5x^2
\]

### Step 2: Combine like terms.
- Combine the constant terms: \(3 - 6 = -3\)
- Combine the linear terms (the terms with \(x\)): \(-4x + 2x = -2x\)
- Combine the quadratic terms (the terms with \(x^2\)): \(8x^2 - 5x^2 = 3x^2\)

### Step 3: Write the simplified polynomial.
Putting this all together, we have:
\[
-3 - 2x + 3x^2
\]

### Final Result
The simplified polynomial is:
\[
3x^2 - 2x - 3
\]

Note: The final result can be arranged as \(3x^2 - 2x - 3\) instead of placing the constant term first.