Mbledhja dhe zbritja e
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This document discusses adding and subtracting polynomials. It provides examples of combining like terms in polynomials and changing signs when subtracting polynomials. It also gives examples of finding the perimeter of shapes by adding or subtracting terms in polynomial expressions.
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Mbledhja dhe zbritja e
- 1. MBLEDHJA DHE ZBRITJA E POLINOMEVE Tefik Rika
- 2. Tefik Rika Identifikimi i polinomit dhe shkalla e tijë Polinomi Emri Shkalla monom konstant binom linear binom linear binom katror trinom katror trinom kubik binom kubik 12 8x – 5 4x + 3 x2 + 6 3x2 + 6x + 5 x3 + 2x – 2 x3 + 4
- 3. Tefik Rika Forma standarde e polinomit:Rradhitja sipas shkallës,duke filluar prej shkallës më të lartë. Polinomi Forma standarde 7 + 2x2 2x2 + 7 x3 + 6x2 9 + x – 4x2 a + a2 + a3 + 1 a3 + a2 + a + 1 – m3 – 3m2 + 2m + 8 6x2 + x3 -4x2 + x + 9 8 – 3m2 – m3 + 2m
- 4. Mbledhja e polinomeve: Forma horizontale: (x2 + 2x + 5) + (3x2 + x + 12)= = 4x2+ 3x + 17 Forma vertikale: x2+ 2x + 5 + 3x2 + x + 12 = 4x2+ 3x + 17 Tefik Rika
- 5. Shembull: x2 + x + 1 + 2x2 + 3x + 2 3x2+ 4x + 3 (4b2 + 2b + 1) + (7b2 + b – 3) 11b2 + 3b – 2 3x2 – 4x + 8 + 2x2 – 7x – 5 5x2 – 11x + 3 a2 + 8a – 5 + 3a2 + 2a – 7 4a2 + 10a – 12 Tefik Rika
- 6. Shembull: 7d2 + 7d + 2d2 + 3d 9d2+ 10d (2x2 – 3x + 5) + (4x2 + 7x – 2) 6x2+ 4x + 3 z2 + 5z + 4 + 2z2 - 5 3z2 + 5z – 1 (a2 + 6a – 4) + (8a2 – 8a) 9a2 – 2a – 4 Tefik Rika
- 7. 9.1 Adding and Subtracting Polynomials Shembull: 3d2 + 5d – 1 + (–4d2 – 5d + 2) –d2+ 1 (3x2 + 5x) + (4 – 6x – 2x2) x2 – x + 4 7p2 + 5 + (–5p2 – 2p + 3) 2p2 – 2p + 8 (x3 + x2 + 7) + (2x2 + 3x – 8) x3 + 3x2 + 3x – 1 Tefik Rika
- 8. 9.1 Adding and Subtracting Polynomials Shembull: 2x3 + x2 – 4 + 3x2 – 9x + 7 2x3 + 4x2 – 9x + 3 5y2 – 3y + 8 + 4y3 – 9 4y3 + 5y2 – 3y – 1 4p2 + 5p + (-2p + p + 7) 4p2 + 4p + 7 (8cd – 3d + 4c) + (-6 + 2cd – 4d) 4c – 7d + 10cd – 6 Tefik Rika
- 9. Shembull: (12y3 + y2 – 8y + 3) + (6y3 – 13y +5)= = 18y3+ y2 – 21y + 8 (7y3 + 2y2 – 5y + 9) + (y3 – y2 + y – 6)= = 8y3 + y2 – 4y + 3 (6x5 + 3x3 – 7x – 8) + (4x4 – 2x2 + 9)= = 6x5+ 4x4 + 3x3 – 2x2 – 7x + 1 Tefik Rika
- 10. Ndryshimi i polinomeve (Vërejtje: Ja shtojmë polinomin e kundërt) (5x2 + 10x + 2) – (x2 – 3x + 12)= =(5x2 + 10x + 2) + (–x2) + (3x) + (–12)= = 4x2+ 13x – 10 5x2 + 10x + 2 4x2+ 13x – 10 –(x2 – 3x + 12) = 5x2 + 10x + 2 = –x2 + 3x – 12 Tefik Rika
- 11. (3x2 – 2x + 8) – (x2 – 4)= =3x2 – 2x + 8 + (–x2) + 4= = 2x2 – 2x + 12 (10z2 + 6z + 5) – (z2 – 8z + 7)= =10z2 + 6z + 5 + (–z2) + 8z + (–7)= = 9z2 + 14z – 2 Tefik Rika
- 12. Shembull: 7a2 – 2a – (5a2 + 3a) 2a2 – 5a 4x2 + 3x + 2 – (2x2 – 3x – 7) 2x2 + 6x + 9 3x2 – 7x + 5 – (x2 + 4x + 7) 2x2 – 11x – 2 7x2 – x + 3 – (3x2 – x – 7) 4x2 + 10 Tefik Rika
- 13. Shembull: 3x2 – 2x + 10 – (2x2 + 4x – 6) x2 – 6x + 16 3x2 – 5x + 3 – (2x2 – x – 4) x2 – 4x + 7 2x2 + 5x – (x2 – 3) x2 + 5x + 3 4x2 – x + 6 – (3x2 – 4) x2 – x + 10 Tefik Rika
- 14. Shembull: (4x5 + 3x3 – 3x – 5) – (– 2x3 + 3x2 + x + 5)= = 4x5 + 5x3 – 3x2 – 4x – 10 (4d4 – 2d2 + 2d + 8) – (5d3 + 7d2 – 3d – 9)= = 4d4 – 5d3 – 9d2 + 5d + 17 (a2 + ab – 3b2) – (b2 + 4a2 – ab)= = –3a2 + 2ab – 4b2 Tefik Rika
- 15. 9.1 Adding and Subtracting Polynomials Cakto perimetrin e figurave: 2x2 B x2 + x 6c + 3 c2 + 1 A 4c2 + 2c + 5 B = 6x2 + 2x A = 5c2 + 8c + 9 2x2 x2 + x Tefik Rika
- 16. Tefik Rika Cakto perimetrin e figurave: 3x2 – 5 x x2 + 7 C 2d2 + d – 4 D d2 + 7 3d2 – 5d 3d2 – 5d C = 8x2 – 10x + 14 D = 9d2 – 9d + 3
- 17. Cakto perimetrin e figurave: x2 + 3 F a + 1 a3 + 2a E 2a3 + a + 3 F = 8x2 – 10x + 6 E = 3a3 + 4a + 4 3x2 – 5x Tefik Rika