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Saturday, March 8, 2008 Section 12.4 (Addition and Subtraction of Polynomials) To add two polynomials, you can just write a plus sign between them and collect like terms Examples: (-4x3 + 1 2 x + 2x – 3) + (8x3 – 2x2 + 8) = 2 (3 – 3x2 + 13x4) + (1 + x + 3x2 + x3) = (note order) You can also add polynomials by writing them in columns Example: (11x2 – x + 4) + (-2x2 – 3) => To find the opposite / additive inverse of a number, we can multiply that same number by negative 1, resulting in changing the sign (opposite of 1 is -1, opposite of -3.2 is 3.2) The same is true with polynomials Examples: Simplify -(7n4 – 5n2 + 4) = -(- 1 5 5 x + 2x3 - x) = 3 2 Subtracting polynomials is equivalent to adding their opposites (just as in real numbers) Examples: (9x5 + 3x3 – 2x + 4) – (7x5 – 11x4 + 3x3 + 1) = (3n2 + 3n + 3) – (-n2 + 2n + 2) = (17x3 + 3x2 – 3) – (x2 – 3) = (use columns) Example: Find a polynomial for the sum of the perimeters and areas of the following rectangles ½x 2x x x 2x x Additional Homework from Book: 4, 7, 11, 18, 25, 29, 35, 37, 39, 42