1. 5.3 Adding and Subtracting Polynomials
Math 9

2. A polynomial is: an algebraic expression made up of terms connected by the operations of addition and/or subtraction
Example:
6x2 – 3xy +7y2 -7

3. Example 1: Add polynomials – give your answers in simplest form
(2a − 1) + (6 − 4a)
2a − − 4a
2a − 4a − 1 + 6
-2a + 5

4. (2a − 1) (6 − 4a)

5. (2a − 1) (6 − 4a)

6. (2a − 1) (6 − 4a)
5 – 2a

7. (3t2 − 5t) + (t2 + 2t + 1)
3t2 − 5t + t2 + 2t + 1
3t2 + t2 − 5t + 2t + 1
4t2 − 3t + 1

8. b) (3t2 − 5t) (t2 + 2t + 1)

9. b) (3t2 − 5t) (t2 + 2t + 1)

10. b) (3t2 − 5t) (t2 + 2t + 1)
4t2 -3t +1

11. Example 2: Opposites of Polynomial Expressions
a) x -x
b) 5 − 3x x
c) 7 x2 + 5x − 1
-7 x2 - 5x + 1
d) −3x3 − 4 x2 + 3x − 2
3x3 + 4 x2 - 3x + 2
When two opposites are combined they are referred to as ZERO PAIRS

12. Recall that when you subtract integers you need to add the opposite
**Recall that when you subtract integers you need to add the opposite. Example (−2) − 3 4 − (−5) (-2)+ (-3) = (+5) = 9

13. Example 3: Subtracting Polynomials – give your answers in simplest form
(2 x − 3) − (− x + 2)
2 x − 3 + (x -2)
2 x − 3 + x + (-2)
2 x + x − 3 + (-2)
3 x − 5

14. (2 x − 3) − (− x + 2)
3 x − 5

15. 5x2 − x + 4 + (-2x2 + 3x + 1) 5x2 + (-2x2) − x + 3x + 4 + 1
b) (5x2 − x + 4) − (2x2 − 3x − 1)
5x2 − x (-2x2 + 3x + 1)
5x2 + (-2x2) − x + 3x
3x2 + 2x + 5

16. (5x2 − x + 4) − (2x2 − 3x − 1)

17. (5x2 − x + 4) − (2x2 − 3x − 1)
3x2 + 2x + 5

18. Example 4 Identify the errors in Sam’s work below and correct them:
(−2x2 + 7) − (3x2 + x − 5)
= (−2x2 + 7) + (−3x2 − x + 5)
= −2x2 − 3x2 − x
= 5x2 − x + 12
= -5x2 − x + 12

19. Partner Jigsaw
5 7abc 8ab 10abc 12

20. Practice
14, 15, 16, 18, 20, 24
TOMORROW
9.2 Quiz
9.3 Assignment