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# 10 1 Adding Subtracting Polynomials

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### 10 1 Adding Subtracting Polynomials

1. 1. Adding & Subtracting Polynomials
2. 2. Adding & Subtracting Polynomials <ul><li>Two methods: </li></ul><ul><li>Horizontal </li></ul><ul><li>Vertical </li></ul>
3. 3. Adding Polynomials <ul><li>Horizontal. </li></ul><ul><li>Group the like terms together. Using a color can be helpful. </li></ul><ul><li>Remember that the sign in front of the number stays with the number. </li></ul>
4. 4. Adding Polynomials <ul><li>(2x 2 – 3x + 4) + (3x 2 + 2x – 3) </li></ul><ul><li>( 2x 2 + 3x 2 ) + ((– 3x) + 2x) + ( 4 + (– 3) ) </li></ul><ul><li>5x 2 – x + 1 </li></ul>
5. 5. Adding Polynomials <ul><li>Vertical </li></ul><ul><li>Line up the like terms. </li></ul><ul><li>Remember that the sign in front of the number stays with the number. </li></ul><ul><li>You may have to rearrange the terms to line them up. </li></ul>
6. 6. Adding Polynomials <ul><li>2x 2 – 3x + 4 </li></ul><ul><li>3x 2 + 2x – 3 </li></ul><ul><li>5x 2 – 1x + 1 </li></ul>
7. 7. Subtracting Polynomials <ul><li>When you are subtracting, go ahead and change all the signs in the second set. </li></ul>
8. 8. Subtracting Polynomials - Horizontal <ul><li>(7x 3 – 3x + 1) - (x 3 + 4x 2 – 2) </li></ul><ul><li>(7x 3 – 3x + 1) + (-x 3 - 4x 2 + 2) </li></ul><ul><li>Now it becomes an addition problem </li></ul><ul><li>(7x 3 – x 3 ) + (-4x 2 ) + (-3x) + (1 + 2) </li></ul><ul><li>6x 3 – 4x 2 – 3x + 3 </li></ul>
9. 9. Subtracting Polynomials - Vertical <ul><li>(7x 3 – 3x + 1) - (x 3 + 4x 2 – 2) </li></ul><ul><li>(7x 3 – 3x + 1) + (-x 3 - 4x 2 + 2) </li></ul><ul><li>Now it becomes an addition problem </li></ul><ul><li>7x 3 – 3x + 1 </li></ul><ul><li>-x 3 - 4x 2 + 2 </li></ul><ul><li>6x 3 -4x 2 - 3x +3 </li></ul>
10. 10. Horizontal or Vertical <ul><li>Both horizontal and vertical have their place. </li></ul><ul><li>You can decide which one to use based on the way the problem is laid out. </li></ul>