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OPERATIONS WITH POLYNOMIALS JUST THE BASICS

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ADDITION AND SUBTRACTION When adding or subtracting polynomials remember they must be exactly the same!!! 5x + 3x = 8x That is okay 5x 2 + 3x ≠ 8x 2 These terms are not the same!!!!

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

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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 (3x 2 – 2x + 1) – (x 2 + 5x – 9)Distribute the negative 1 st. 3x 2 – 2x + 1 – x 2 - 5x + 9Combine like terms! 2x 2 – 7x + 10 Example 2 (-7x 2 – x + 5) - (2 – x 3 + 3x)Distribute. -7x 2 – x + 5 – 2 + x 3 – 3x Combine like terms x 3 – 7x 2 – 4x + 3 Traditionally, the terms would be written highest power to lowest. I do not really care!!!

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

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TRY ON YOUR OWN 1.Find a partner. 2.Work the problems on the board. 3.Take turns working out the problems. 4.I will give you about 15 minutes and then show you the answers.

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6.1 Review of the Rules for Exponents

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