MBLEDHJA DHE ZBRITJA E POLINOMEVE

Tefik Rika

Polinomi Emri Shkalla

monom konstant binom linear

binom linear

binom katror

trinom katror

trinom kubik

Identifikimi i polinomit dhe shkalla e tijë

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

– m3 – 3m2 + 2m + 8

6x2 + x3

-4x2 + x + 9

8 – 3m2 – m3 + 2m

a + a2 + a3 + 1 a3 + a2 + a + 1

Tefik Rika

Mbledhja e polinomeve:

= 4x2+ 3x + 17

(x2 + 2x + 5) + (3x2 + x + 12)=Forma horizontale:

x2+ 2x + 53x2 + x + 12+

= 4x2+ 3x + 17

Forma vertikale:

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

Shembull: 3d2 + 5d – 1

+ (–4d2 – 5d + 2)

–d2+ 1

(3x2 + 5x)

+ (4 – 6x – 2x2)

x2 – x + 4

9.1 Adding and Subtracting Polynomials

7p2 + 5+ (–5p2 – 2p + 3)

2p2 – 2p + 8

(x3 + x2 + 7)

+ (2x2 + 3x – 8)

x3 + 3x2 + 3x – 1

Tefik Rika

Shembull:

2x3 + x2 – 4+ 3x2 – 9x + 7

2x3 + 4x2 – 9x + 3

5y2 – 3y + 8

+ 4y3 – 9

4y3 + 5y2 – 3y – 1

9.1 Adding and Subtracting Polynomials

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)=

(7y3 + 2y2 – 5y + 9) + (y3 – y2 + y – 6)=

(6x5 + 3x3 – 7x – 8) + (4x4 – 2x2 + 9)=

= 18y3 + y2 – 21y + 8

= 8y3 + y2 – 4y + 3

= 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)=

5x2 + 10x + 2

4x2+ 13x – 10

–(x2 – 3x + 12)

= 4x2+ 13x – 10

= 5x2 + 10x + 2 = –x2 + 3x – 12

Tefik Rika

= 2x2 – 2x + 12

(3x2 – 2x + 8) – (x2 – 4)=

=3x2 – 2x + 8 + (–x2) + 4=

(10z2 + 6z + 5) – (z2 – 8z + 7)=

=10z2 + 6z + 5 + (–z2) + 8z + (–7)=

= 9z2 + 14z – 2

Tefik Rika

Shembull:

7a2 – 2a

2a2 – 5a

– (5a2 + 3a)

4x2 + 3x + 2

2x2 + 6x + 9 – (2x2 – 3x – 7)

3x2 – 7x + 5

2x2 – 11x – 2

– (x2 + 4x + 7)

7x2 – x + 3

4x2 + 10

– (3x2 – x – 7)

Tefik Rika

Shembull:

3x2 – 2x + 10

x2 – 6x + 16

– (2x2 + 4x – 6)

3x2 – 5x + 3

x2 – 4x + 7 – (2x2 – x – 4)

2x2 + 5x

x2 + 5x + 3

– (x2 – 3)

4x2 – x + 6

x2 – x + 10

– (3x2 – 4)

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

Cakto perimetrin e figurave:

x2 + x

2x2 B

6c + 3

4c2 + 2c + 5

c2 + 1

B = 6x2 + 2xA = 5c2 + 8c + 9

A

9.1 Adding and Subtracting Polynomials

2x2

x2 + x

Tefik Rika

3x2 – 5 x

x2 + 7 C

D

2d2 + d – 4

d2 + 7

3d2 – 5d

C = 8x2 – 10x + 14 D = 9d2 – 9d + 3

3d2 – 5d

Cakto perimetrin e figurave:

Tefik Rika

x2 + 3 Fa + 1

2a3 + a + 3

a3 + 2a

F = 8x2 – 10x + 6 E = 3a3 + 4a + 4

E

3x2 – 5x

Cakto perimetrin e figurave:

Tefik Rika