1. Adding and Subtracting Polynomials 1/6/2014

2. Example 1 Add Polynomials Vertically a. Add and 2x 32x 3 x9 + 4x 24x 2 + – x 3x 3 5x5x1 6x 26x 2 – + – 3x 33x 3 4x4x8 2x 22x 2 – ++ SOLUTION 2x 32x 3 x9 + 4x 24x 2 + – x 3x 3 5x5x1 6x 26x 2 – + – + a.

3. Example 1 Add Polynomials Horizontally b. Add and 5x 25x 2 2x2x + 4x 24x 2 3 7x7x – + 5x 25x 2 4x 24x 2 + 2x2x 3 7x7x – ++ = 9x 29x 2 3 5x5x – + = Group like terms. Combine like terms.

4. Example 2 Subtract Polynomials SOLUTION Align like terms, then add the opposite of the subtracted polynomial. 6x 36x 3 7x7x12 x 2x 2 – + – 3x 33x 3 9x9x 4x 24x 2 + ––– 3x 33x 3 2x2x 5x 25x 2 –– –

5. Example 3 Use the Distributive Property Simplify the expression. 2x 22x 2 5 x – + x 2x 2 7 3x3x + – ()() + 42 14 6x6x + 8x 28x 2 20 4x4x – = – Use distributive property. ++ 2x 22x 2 6x6x + 8x 28x 2 4x4x 2x 22x 2 – = Group like terms. ++ 20 – 14 10x 2 = Combine like terms. 2x2x + 6 + a.

6. Example 3 Use the Distributive Property = Use distributive property. x 4x 4 x 3x 3 ++ x 2x 2 x + x 3x 3 x 2x 2 x + –– 1 – = Group like terms. x 4x 4 x 3x 3 ++ 1 + x 3x 3 – x 2x 2 + x 2x 2 – xx – = Combine like terms. x 4x 4 2x2x + 1 –

7. Homework: WS: Adding/Subtracting Polynomials