Addition and Subtraction of Polynomials
- 2. OBJECTIVES: At the end of the lesson the students must be able to; 1.Add polynomials 2.Subtract polynomials; and 3.Solve problems involving adding and subtracting polynomials.
- 4. 1. What is the sum of 3x2 + 5x- 9 and -3x+4? a) 8x - 13 b) 3x2 - 2x +5 c) 3x2 + 2x- 5 d) -3x2 -3x
- 5. 2. Subtract2x+2 from 9x+1 b) 11x-3 c) 7x-1 d) 11x a) 7x-2
- 7. Algebraic Expressions Like Terms Unlik e Term s x , 2x, 3x, 4x 2x2, 2y2 2x, 2y 4xy2, xy2 6b, 6b3 2x2y, 2xy2 Put a check whether the expressions are like terms or unlike terms
- 8. Like Terms or Similar Terms are algebraic expressions with the same variables and exponent regardless of numerical coefficient
- 9. Familiarize yourself with the Tiles below: Stands for +1 Stands for - 1 Stands for +x Stands for - x Stands for + x2 Stands for - x2 Can you represent the following quantities using the tiles above? 1. x – 2 2. 4x +1
- 10. x – 2 Is the same as
- 11. 4x +1 Is the same as:
- 12. ACTIVITY 2 Represent the following quantities using the tiles. *3𝑥2 + 𝑥 − 2 *−2𝑥2 − 𝑥
- 13. To add polynomials group like terms horizontally or write them in column form, aligning like terms. (3x2 – 4x + 8) + (2x – 7x2 – 5) Method 1: horizontal Group like terms. (3x2 – 7x2) + (-4x + 2x) + (8 – 5) add like terms. -4x2 – 2x + 3
- 14. Method 2: Vertical 3x2 – 4x + 8 + -7x2 + 2x -5 - 4x2 – 2x + 3 Notice that terms are in descending order with like terms aligned.
- 15. 1. What is the sum of 3x2 + 5x- 9 and -3x+4? a) 8x - 13 b) 3x2 - 2x +5 c) 3x2 + 2x- 5 d) -3x2 -3x
- 16. Activity 3 Add *(4𝑦3 + 9y − 11) + (2𝑦2 − 3𝑦)
- 17. Activity 3 Add *( −𝟓𝒙𝟐 + 𝟏𝟎𝒙 𝒚 + 𝟒𝒚𝟐 ) + (𝟕𝒙𝟐 + 𝟖 × 𝒚 − 𝟔𝒚𝟐 )
- 18. 2x2 – 15x + 25 3x2 + 12x – 18 - 2x2 – 15x + 25 -3x2 - 12x + 18 + -x2 – 27x + 43 Ex. (2x2 – 15x + 25) – (3x2 + 12x – 18) CHANGE KEEP CHANGE In subtracting polynomials, always remember the KEEP, CHANGE, CHANGE process, then proceed to addition rule.
- 19. 2. (30x3 – 50x2 + 20x – 80) – (17x3 + 26x + 19) - 17x3 + 26x + 19 30x3 – 50x2 + 20x - 80 30x3 – 50x2 + 20x - 80 -17x3 - 26x - 19 + 13x3 – 50x2 - 6x - 99 . In subtracting polynomials, always remember the KEEP, CHANGE, CHANGE process, then proceed to addition rule
- 20. . *Example If you have (100𝑥3 − 5𝑥2 + 3) pesos in your wallet and spent 80𝑥3 − 2𝑥2 + 9 pesos in your school canteen, how much money lest in your pocket? Solution: (100𝑥3 − 5𝑥2 + 3) - 80𝑥3 − 2𝑥2 + 9 (100𝑥3 − 5𝑥2 + 3) + −80𝑥3 + 2𝑥2 − 9 𝟐𝟎𝒙𝟑 − 𝟑𝒙𝟐 − 𝟔
- 21. 2. Subtract2x+2 from 9x+1 b) 11x-3 c) 7x-1 d) 11x a) 7x-2
- 23. Subtract . *What must be added to 5x-8 to get a result of 10x + 11?
- 24. Subtract . *Mary saved 3𝑥2 + 17𝑥 − 10 from her allowance. How much did she have after buying a gift worth 10x+7 for her sister’s birthday?