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MBLEDHJA DHE ZBRITJA E 
POLINOMEVE 
Tefik Rika
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
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
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
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
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
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
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
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
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
(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
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
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
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
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
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
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

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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