Adding and subtracting polynomials
- 1. Adding and Subtracting Polynomials Presentation by E Whitener Using PowerPoint All Images sourced at: pixabay.com CC0 Public Domain text added by ewhitener
- 2. Let’s take a look at this example of adding polynomials. (3x2 + 5 – 2x) + (5x + 4x2 – 2) (3x2 – 2x + 5) + (4x2 + 5x – 2) 3x2 – 2x + 5 4x2 + 5x – 2 7x2 + 3x + 3 1. Re arrange the terms Exponents in decreasing order. 2. Stack the polynomials. Be sure you match the like terms, same variable and exponent. 3. Combine like terms Notice: The variable and exponents DO NOT change
- 3. (–8x + x2 + 4 ) + (5x – 6 - 3x2) (x2 – 8x + 4) + (-3x2 + 5x – 6) x2 – 8x + 4 -3x2 + 5x – 6 -2x2 - 3x – 2 Now another example! 1. Re arrange the terms. 2. Stack the polynomials. 3. Combine like terms.
- 4. Now we will look at how to subtract polynomials. To subtract polynomials, you will need to use the definition of subtraction! Subtraction is adding the opposite, for example: becomes becomes becomes becomes Created by eWhitener using Word
- 5. Let’s see how all these pieces fit together. Stack Polynomials
- 6. Now let’s look at an example of subtracting polynomials. (6x2 + 11x – 3) – (3x2 - 5x + 9) (6x2 + 11x – 3) + (-3x2 + 5x - 9) 6x2 + 11x – 3 -3x2 + 5x - 9 3x2 + 16x - 12 1. Add the opposite of each term . Change each sign in the 2nd polynomial. 2. Stack the polynomials. Put like terms together just like for addition. 3. Combine like terms.
- 7. If you change subtraction to adding the opposite, then you can combine like terms! (x2 + 7x – 7) – (3x2 - 5x + 3) (x2 + 7x – 7) + (-3x2 + 5x -3) x2 + 7x – 7 -3x2 + 5x -3 -2x2 + 5x -10 1. Add the opposite of each term . 2. Stack the polynomials. 3. Combine like terms.
- 8. So. . . now you see that if you know how to add polynomials, you know how to subtract polynomials! All Images sourced at: pixabay.com CC0 Public Domain text added by ewhitener