Adding and Subtracting Polynomials

Sure, here's how to add and subtract polynomials:

Step 1: Identify the polynomials that need to be added or subtracted.

For example, let's take two polynomials: P(x) = 2x^3 - 5x^2 + 3x - 2 and Q(x) = x^3 + 4x^2 - x + 6.

Step 2: Arrange the polynomials vertically by aligning like terms, i.e., terms with the same power of x.

P(x) = 2x^3 - 5x^2 + 3x - 2 Q(x) = x^3 + 4x^2 - x + 6

Step 3: Add or subtract the coefficients of the like terms.

If we're adding P(x) and Q(x), we get:

R(x) = (2x^3 + x^3) + (-5x^2 + 4x^2) + (3x - x) + (-2 + 6) = 3x^3 - x^2 + 2x + 4

If we're subtracting Q(x) from P(x), we get:

R(x) = (2x^3 - x^3) + (-5x^2 - 4x^2) + (3x - (-x)) + (-2 - 6) = x^3 - 9x^2 + 4x - 8

So, the result of adding P(x) and Q(x) is 3x^3 - x^2 + 2x + 4, and the result of subtracting Q(x) from P(x) is x^3 - 9x^2 + 4x - 8.