x^9 + x^8 + x^7 - x^3 + 1 

= x^7 ( x^2 + x + 1 ) - ( x^3 - 1 )

= x^7 ( x^2 + x + 1 ) - ( x - 1 )(x^2 + x +   1 )

= ( x^7 - x + 1 )(x^2 + x + 1 ) 

 x⁷ + x² + 1 = (x⁷ – x) + (x² + x + 1) 
= x.(x⁶ – 1) + (x² + x +1) 
= x.(x³ - 1).(x³ +1) + (x² + x +1) 
= x.(x-1).(x² + x +1).(x³ +1) + (x²+ x +1) 
= (x² + x +1).[x.(x-1).(x³ +1) + 1] 
= (x² + x +1).[(x²-x).(x³ +1) + 1] 
= (x² + x +1).(x⁵-x⁴ + x² -x + 1)

x7 + x2 + 1 = (x7 – x) + (x2 + x + 1) 
= x.(x6 – 1) + (x2 + x +1) 
= x.(x3 - 1).(x3 +1) + (x2 + x +1) 
= x.(x-1).(x2 + x +1).(x3 +1) + (x2 + x +1) 
= (x2 + x +1).[x.(x-1).(x3 +1) + 1] 
= (x2 + x +1).[(x2-x).(x3 +1) + 1] 
= (x2 + x +1).(x5-x4 + x2 -x + 1)

(3x+2)(2x+9)-(x+2)(6x+1)=(x+1)-(x-6)

<=>(6x²+27x+4x+18)-(6x²+x+12x+2)=x+1-x+6

<=>6x²+31x+18-6x²-13x-2=7

<=>18x+16=7

<=>18x=-9

<=>x=-1/2

 x^5 - x^4 - 1 

= x^5 - x^3 - x² - x^4 + x² + x + x^3 - x - 1 

= x²( x^3 - x - 1 ) - x( x^3 - x - 1 ) + ( x^3 - x - 1 ) 

= ( x² - x + 1)( x^3 - x - 1 )

x⁵-x⁴-1=x⁵-x⁴+x³-x³-1=x³(x²-x+1)-(x³+1)=x³(x²-x+1)-(x+1)(x²-x+1)=(x³-1)(x²-x+1)=(x-1)(x²+x+1)(x²-x+1)

=x⁵+x²-x²+x-1

=x²(x³+1)-(x²-x+1)

=x²(x+1)(x²-x+1)-(x²-x+1)

=(x²-x+1)[x²(x+1)-1]

=(x²-x+1)(x³+x²-1)

= ( 3²⁵)² - 1  +  2

= ( 3²⁵ - 1) ( 3²⁵ + 1) + 2

=> ko phải

Đặt x^2 + x = t 

Thay vào ta có đa thức mới :

    t. ( t + 1 ) - 6 

= t^2 + t - 6 

= t^2 + 2t  - 3t - 6 

= t.(t+2 ) - 3 .(t+2)

= ( t - 3 )(t + 2 )

Thay t = x^2 + x ta có :

= ( x^2 + x - 3 )(x^2 + x + 2 ) 

  x²(x-3)-4(x-3)=0

(x-3)(x²-4)=0

(x-3)(x+2)(x-2)=0

=>x-3=0 hoac x+2=0 hoac x-2=0

x=3 hoac x=-2 hoac x=2

 x²(x-3)-4(x-3)=0
(x-3)(x2
-4)=0
(x-3)(x+2)(x-2)=0
=>x-3=0 hoac x+2=0 hoac x-2=0
x=3 hoac x=-2 hoac x=2

:3