1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Objective: The learner will.., Write polynomials in standard form, Add and Subtract polynomials, by combining or subtracting like terms 9.1 Adding and Subtracting Polynomials NCSCOS 1.01

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) 9.1 Adding and Subtracting Polynomials PolynomialNameName by Degree monomial constant binomial linear binomial quadratic trinomial quadratic trinomial cubic Identify each polynomial by the name and degree binomial cubic 12 8x – 5 4x + 3 x 2 + 6 3x 2 + 6x + 5 x 3 + 2x – 2 x 3 + 4

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Standard form: the terms of the polynomial are in descending order, meaning, the greatest exponent to the smallest (left to right). 9.1 Adding and Subtracting Polynomials Polynomial Standard Form 7 + 2x 2 2x 2 + 7 x 3 + 6x 2 9 + x – 4x 2 – m 3 – 3m 2 + 2m + 8 6x 2 + x 3 -4x 2 + x + 9 8 – 3m 2 – m 3 + 2m a + a 2 + a 3 + 1 a 3 + a 2 + a + 1

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Adding Polynomials = 4x 2 + 3x + 17 9.1 Adding and Subtracting Polynomials (x 2 + 2x + 5) + (3x 2 + x + 12) in horizontal form: x 2 + 2x + 5 3 x 2 + x + 12 + = 4 x 2 + 3x + 17 in vertical form:

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Simplify: x 2 + x + 1 + 2x 2 + 3x + 2 3x 2 + 4x + 3 (4b 2 + 2b + 1) + (7b 2 + b – 3) 11b 2 + 3b – 2 9.1 Adding and Subtracting Polynomials 3x 2 – 4x + 8 + 2x 2 – 7x – 5 5x 2 – 11x + 3 a 2 + 8a – 5 + 3a 2 + 2a – 7 4a 2 + 10a – 12

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Simplify: 7d 2 + 7d + 2d 2 + 3d 9d 2 + 10d (2x 2 – 3x + 5) + (4x 2 + 7x – 2) 6x 2 + 4x + 3 9.1 Adding and Subtracting Polynomials z 2 + 5z + 4 + 2z 2 - 5 3z 2 + 5z – 1 (a 2 + 6a – 4) + (8a 2 – 8a) 9a 2 – 2a – 4

7. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Simplify: 3d 2 + 5d – 1 + ( – 4d 2 – 5d + 2) – d 2 + 1 (3x 2 + 5x) + (4 – 6x – 2x 2 ) x 2 – x + 4 9.1 Adding and Subtracting Polynomials 7p 2 + 5 + (–5p 2 – 2p + 3) 2p 2 – 2p + 8 (x 3 + x 2 + 7) + (2x 2 + 3x – 8) x 3 + 3x 2 + 3x – 1

8. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Simplify: 2x 3 + x 2 – 4 + 3x 2 – 9x + 7 2x 3 + 4x 2 – 9x + 3 5y 2 – 3y + 8 + 4y 3 – 9 4y 3 + 5y 2 – 3y – 1 9.1 Adding and Subtracting Polynomials 4p 2 + 5p + (-2p + p + 7) 4p 2 + 4p + 7 (8cd – 3d + 4c) + (-6 + 2cd – 4d) 4c – 7d + 10cd – 6

9. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Simplify: (12y 3 + y 2 – 8y + 3) + (6y 3 – 13y + 5) (7y 3 + 2y 2 – 5y + 9) + (y 3 – y 2 + y – 6) (6x 5 + 3x 3 – 7x – 8) + (4x 4 – 2x 2 + 9) = 18y 3 + y 2 – 21y + 8 9.1 Adding and Subtracting Polynomials = 8y 3 + y 2 – 4y + 3 = 6x 5 + 4x 4 + 3x 3 – 2x 2 – 7x + 1

10. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Subtracting Polynomials (Note: subtraction is adding the opposite) (5x 2 + 10x + 2) – (x 2 – 3x + 12) (5x 2 + 10x + 2) + (–x 2 ) + (3x) + (–12) 5x 2 + 10x + 2 4x 2 + 13x – 10 –(x 2 – 3x + 12) 9.1 Adding and Subtracting Polynomials = 4x 2 + 13x – 10 = 5x 2 + 10x + 2 = –x 2 + 3x – 12

11. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Simplify: 9.1 Adding and Subtracting Polynomials = 2x 2 – 2x + 12 (3x 2 – 2x + 8) – (x 2 – 4) 3x 2 – 2x + 8 + (–x 2 ) + 4 (10z 2 + 6z + 5) – (z 2 – 8z + 7) 10z 2 + 6z + 5 + (–z 2 ) + 8z + (–7) = 9z 2 + 14z – 2

12. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Simplify: 7a 2 – 2a 2a 2 – 5a – (5a 2 + 3a) 9.1 Adding and Subtracting Polynomials 4x 2 + 3x + 2 2x 2 + 6x + 9 – (2x 2 – 3x – 7) 3x 2 – 7x + 5 2x 2 – 11x – 2 – (x 2 + 4x + 7) 7x 2 – x + 3 4x 2 + 10 – (3x 2 – x – 7)

13. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Simplify: 3x 2 – 2x + 10 x 2 – 6x + 16 – (2x 2 + 4x – 6) 9.1 Adding and Subtracting Polynomials 3x 2 – 5x + 3 x 2 – 4x + 7 – (2x 2 – x – 4) 2x 2 + 5x x 2 + 5x + 3 – (x 2 – 3) 4x 2 – x + 6 x 2 – x + 10 – (3x 2 – 4)

14. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Simplify: (4x 5 + 3x 3 – 3x – 5) – (– 2x 3 + 3x 2 + x + 5) = 4x 5 + 5x 3 – 3x 2 – 4x – 10 9.1 Adding and Subtracting Polynomials (4d 4 – 2d 2 + 2d + 8) – (5d 3 + 7d 2 – 3d – 9) = 4d 4 – 5d 3 – 9d 2 + 5d + 17 (a 2 + ab – 3b 2 ) – (b 2 + 4a 2 – ab) = –3a 2 + 2ab – 4b 2

15. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) Simplify by finding the perimeter: x 2 + x 2x 2 B 6c + 3 4c 2 + 2c + 5 c 2 + 1 B = 6x 2 + 2x A = 5c 2 + 8c + 9 A 9.1 Adding and Subtracting Polynomials 2x 2 x 2 + x

16. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) 3x 2 – 5 x x 2 + 7 C D 2d 2 + d – 4 d 2 + 7 3d 2 – 5d C = 8x 2 – 10x + 14 D = 9d 2 – 9d + 3 3d 2 – 5d 9.1 Adding and Subtracting Polynomials Simplify by finding the perimeter:

17. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional Slides Created/Edited by Mr. Weidinger, EWHS, Goldsboro, NC) x 2 + 3 F a + 1 2a 3 + a + 3 a 3 + 2a F = 8x 2 – 10x + 6 E = 3a 3 + 4a + 4 E 9.1 Adding and Subtracting Polynomials 3x 2 – 5x Simplify by finding the perimeter: