1. Operations with Polynomials
Just the basics

2. Addition and subtraction
When adding or subtracting polynomials remember they must be exactly the same!!! 5x + 3x = 8x That is okay 5x2 + 3x ≠ 8x2 These terms are not the same!!!!

3. Addition
Example 1 (5x2 – 2x + 3) + (3x2 – 4x2 + 7) Combine like terms within parentheses 1st (5x2 – 2x + 3) + (-x2 + 7) Drop the parentheses and combine like terms. 4x2 – 2x + 10 Example 2 (3x2 + 5x – 2x5) + (6x3 – x2 + 11) Anything the same inside? Nope! Drop the parentheses and combine like terms. -2x5 + 6x3 + 2x2 + 5x + 11

4. Subtraction
Pretty much the same, but before you drop the parentheses you have to distribute the negative sign. (Subtraction sign and negative are interchangeable!) Example 1 (3x2 – 2x + 1) – (x2 + 5x – 9) Distribute the negative 1st. 3x2 – 2x + 1 – x2 - 5x + 9 Combine like terms! 2x2 – 7x + 10 Example 2 (-7x2 – x + 5) - (2 – x3 + 3x) Distribute. -7x2 – x + 5 – 2 + x3 – 3x Combine like terms x3 – 7x2 – 4x + 3 Put in order of decreasing exponents

5. Multiplication
Only rule to remember is that when you multiple variables, you add the exponents. Example 1 Example 2 (-5x3)(9x2) = 5x2(3x5 – x3 + 7x – 4) = -45x5 15x7 – 5x5 + 35x3 -20x2 Example 3 (2x – 5)(x2 – 2x + 3) Distribute in two steps. 2x3 – 4x2 + 6x -5x2 +10x -15 Combine like terms. 2x3 – 9x2 + 16x - 15

6. Try on your own