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Operations with Polynomials

Operations with Polynomials. Just the basics. 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!!!!. Addition. Example 1

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Operations with Polynomials

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  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 Traditionally, the terms would be written highest power to lowest. I do not really care!!!

  5. Multiplication • Only rule to remember is that when you multiple variables, you add the exponents. • Example 1 Example 2 • (-5x3)(9x2) = -45x5 5x2(3x5 – x3 + 7x – 4)= • 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 • Find a partner. • Get a worksheet. • Take turns working out the problems on the worksheet. • Support your partner on their turn. • Check your answers when you are done. • If you are right, get your homework. If not, find another group that can help you!!!

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