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.