This document discusses two methods for adding and subtracting polynomials: 1) The horizontal method involves grouping like terms together and keeping the signs with each term. 2) The vertical method lines up like terms and keeps the signs with each term. To subtract polynomials, change all the signs in the second set and then add the polynomials as if it were an addition problem. Either the horizontal or vertical method can be used, depending on how the problem is laid out.

1. Adding & Subtracting Polynomials

2. Adding & Subtracting Polynomials Two methods: Horizontal Vertical

3. Adding Polynomials Horizontal. Group the like terms together. Using a color can be helpful. Remember that the sign in front of the number stays with the number.

4. Adding Polynomials (2x 2 – 3x + 4) + (3x 2 + 2x – 3) ( 2x 2 + 3x 2 ) + ((– 3x) + 2x) + ( 4 + (– 3) ) 5x 2 – x + 1

5. Adding Polynomials Vertical Line up the like terms. Remember that the sign in front of the number stays with the number. You may have to rearrange the terms to line them up.

6. Adding Polynomials 2x 2 – 3x + 4 3x 2 + 2x – 3 5x 2 – 1x + 1

7. Subtracting Polynomials When you are subtracting, go ahead and change all the signs in the second set.

8. Subtracting Polynomials - Horizontal (7x 3 – 3x + 1) - (x 3 + 4x 2 – 2) (7x 3 – 3x + 1) + (-x 3 - 4x 2 + 2) Now it becomes an addition problem (7x 3 – x 3 ) + (-4x 2 ) + (-3x) + (1 + 2) 6x 3 – 4x 2 – 3x + 3

9. Subtracting Polynomials - Vertical (7x 3 – 3x + 1) - (x 3 + 4x 2 – 2) (7x 3 – 3x + 1) + (-x 3 - 4x 2 + 2) Now it becomes an addition problem 7x 3 – 3x + 1 -x 3 - 4x 2 + 2 6x 3 -4x 2 - 3x +3

10. Horizontal or Vertical Both horizontal and vertical have their place. You can decide which one to use based on the way the problem is laid out.