The document provides a guide on adding, subtracting, and multiplying polynomials, emphasizing the importance of combining like terms. It includes examples to illustrate each operation, such as changing signs for subtraction and using the distributive property for multiplication. The content aims to simplify polynomial operations for better understanding.

1. Polynomials

2. Adding and Subtracting Polynomials

3. Adding Polynomials To add polynomials, combine like terms. + + + = = 2 2 2 Does not =

4. Example Add (-7z 2 + 9z – 3) + (8z 2 – 6z + 9) (-7z 2 + 9z – 3) + (8z 2 – 6z + 9) = -7z 2 + 8z 2 + 9z – 6z – 3 + 9 = 1z 2 + 3z + 6 = z 2 + 3z + 6 Rearrange the terms so that the like terms are grouped together. Add like terms. 1z 2 = z 2

5. Finding the Opposite of a Polynomial When a negative sign precedes parentheses, we find the opposite of the expression by changing the sign of each term inside the parentheses.

6. Example Simplify. –(–5a + 3b – 7c) – (–5a + 3b – 7c) = We change the sign of each term 5a 3b 7c – + – in front of parentheses

7. Subtracting Two Polynomials To subtract two polynomials, change the sign of each term in the second polynomial and then add.

8. Example Perform the operations indicated. (3a 2 + 4a – 7) – (7a 2 – 2a – 5) = 3a 2 + 4a – 7 + ( – 7a 2 ) + 2a + 5 A – sign in front of parentheses indicates we are subtracting. We change the sign of terms that were inside parentheses, then add. = 3a 2 + 4a – 7 + (– 7a 2 ) + 2a + 5 Simplify by combining like terms. = -4a 2 + 6a – 2

9. Multiplying Polynomials

10. Example Multiply. -2y(5y 2 + 3y – 8) -2y (5y 2 + 3y – 8) = -2y (5y 2 ) – 2y (3y) – 2y (– 8) Multiply each term by -2y = -10y 3 – 6y 2 + 16y

11. Example Multiply. (3x + 1)(x - 2) First F Outer O Inner I Last L 3x 2 - 6x x - 2 (3x + 1)(x – 2) = 3x 2 – 5x - 2 Combine like terms. (3x + 1) (x - 2) First Outer Inner Last

12. I hope you enjoyed this short presentation on Polynomials