91Ó°ÊÓ

In the vertical method, align the polynomials so that like terms (terms with the same degree) are in the same column: 3x^2 + 2x - 4 + x^2 - 3x + 2 ------------------------------------------

Now, we can either add or subtract the like terms: For addition: + (3x^2 + x^2) + (2x - 3x) + (-4 + 2) + 4x^2 + (-1x) + (-2) So, P(x) + Q(x) = 4x^2 - x - 2 For subtraction: + (3x^2 - x^2) + (2x + 3x) - (-4 - 2) + 2x^2 + (5x) + (-6) So, P(x) - Q(x) = 2x^2 + 5x - 6

In the horizontal method, write the polynomials in a row: For addition: P(x) + Q(x) = (3x^2 + 2x - 4) + (x^2 - 3x + 2) For subtraction: P(x) - Q(x) = (3x^2 + 2x - 4) - (x^2 - 3x + 2)

Now, combine the like terms: For addition: P(x) + Q(x) = 3x^2 + 2x - 4 + x^2 - 3x + 2 = 4x^2 - x - 2 For subtraction: First, distribute the negative sign: P(x) - Q(x) = 3x^2 + 2x - 4 - x^2 + 3x - 2 Now, combine like terms: P(x) - Q(x) = 2x^2 + 5x - 6 Having explained both methods, let's compare their pros and cons: - Vertical Method: Pros: Easier to see like terms and prevent mistakes when adding or subtracting coefficients. Cons: Requires more space. - Horizontal Method: Pros: Uses less space and can be visually simpler. Cons: Easier to miss like terms and make mistakes when adding or subtracting coefficients. Now that you understand the differences between adding and subtracting polynomials vertically and horizontally, you can decide which method you prefer based on your personal preferences and how you best understand the process.