16. Բեզուի թեորեմ

Վարժ․ 264

ա) 2x³+x²+3

2x³+x²+3/x-1=2x²+3x+3 ⁽⁶⁾

2x³+x²+3=(x-1)(2x²+3x+3)+6

բ) x⁴-2x³+3x²+4x-1

x⁴-2x³+3x²+4x-1/x-1=x³-x²+4x+8 ⁽⁷⁾

x⁴-2x³+3x²+4x-1=(x-1)(x³-x²+4x+8)+7

գ) 4x³+5x²-3x+2

4x³+5x²-3x+2/x-1=4x²+9x+6 ⁽⁸⁾

4x³+5x²-3x+2=(x-1)(4x²+9x+6)+8

դ) x⁵-3x²+3x-10

x⁵-3x²+3x-10/x-1=x⁴+x³-2x²-2x+1 ^(-9)

x⁵-3x²+3x-10=(x-1)(x⁴+x³-2x²-2x+1)-9

Վարժ․ 265

ա) 5x³-3x²+2

(x-1)=> 5-3+2=4

(x+1)= -5-3+2= -6

բ) 2x⁴-3x³-4x²+5x-6

(x-1)=> 2-3-4+5-6= -6

(x+1)=> 2-(-3)-4+(-5)-6= -10

գ) 3x³+2x²-6x+7

(x-1)=> 3+2-6+7=6

(x+1)=> -3+2-(-6)+7=12

դ) 3x⁵-4x²-3x+6

(x-1)=> 3-4-3+6=2

(x+1)= -3-4-(-3)+6=2

Վարժ․ 267

ա) x³+2x²-x-2=0

(1; -1; 2; -2)

x³+2x²-x-2/x-1=x²+3x+2

(x-1)(x²+3x+2)=0=> [ x-1=0; x²+3x+2=0=> [ x=1; x²+3x+2=0 (1)

x²+3x+2=0

D=9-8=1

[ x= -3-1/2; x= -3+1/2=> [ x= -4/2; x= -2/2=> [ x= -2; x= -1

(1)=> [ x=1; x= -2; x= -1

Պատ՝․ -2; -1; 1

բ) x³+6x²+11x+6=0

(1; -1; 2; -2; 3; -3; 6; -6)

x³+6x²+11x+6/x+1=x²+5x+6

(x+1)(x²+5x+6)=0=> [ x+1=0; x²+5x+6=0=> [ x= -1; x²+5x+6=0 (1)

x²+5x+6=0

D=25-24=1

[ x= -5-1/2; x= -5+1/2=> [ x= -6/2; x= -4/2=> [ x= -3; x= -2

(1)=> [ x= -1; x= -2; x= -3

Պատ՝․ -1; -2; -3

գ) x³-2x²-2x-3=0

(1; -1; 3; -3)

x³-2x²-2x-3/x-3=x²+x+1

(x-3)(x²+x+1)=0=> [ x-3=0; x²+x+1=0=> [ x=3; x²+x+1=0 (1)

x²+x+1

D=1-4= -3 (Ø)

(1)=> x=3

Պատ՝․ 3

դ) x³+x²-x+2=0

(1; -1; 2; -2)

x³+x²-x+2/x+2=x²-x+1

(x+2)(x²-x+1)=0=> [ x+2=0; x²-x+1=0=> [ x= -2; x²-x+1=0 (1)

x²-x+1=0

D=1-4= -3 (Ø)

(1)=> x= -2

Պատ՝․ -2

ե) x³+2x²-7x+4=0

(1; -1; 2; -2; 4; -4)

x³+2x²-7x+4/x-1=x²+3x-4

(x-1)(x²+3x-4)=0=> [ x-1=0; x²+3x-4=0=> [ x=1; x²+3x-4=0 (1)

x²+3x-4=0

D=9-(-16)=25

[ x= -3-5/2; x= -3+5/2=> [ x= -8/2; x=2/2=> [ x= -4; x=1

(1)=> [ x=1; x= -4

Պատ՝․ 1; -4

զ) x³-5x²+8x-4=0

(1; -1; 2; -2; 4; -4)

x³-5x²+8x-4/x-1=x²-4x+4

(x-1)(x²-4x+4)=0=> [ x-1=0; x²-4x+4=0=> [ x=1; x²-4x+4=0 (1)

x²-4x+4=0

D=16-16=0

x=4/2=2

(1)=> [ x=1; x=2

Պատ՝․ 1; 2