\(=\left(x^2+x\right)^2+3\left(x^2+x\right)+2-12\)

\(=\left(x^2+x\right)^2+3\left(x^2+x\right)-10\)

\(=\left(x^2+x+5\right)\left(x^2+x-2\right)\)

\(=\left(x^2+x+5\right)\left(x+2\right)\left(x-1\right)\)

x^5+x+1

=x(x^4+1)+1 

=(x^2+x+1)(x^3-x^2+1) 

Ta có : x⁵ + x + 1 

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

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

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

= (x + 1)(x⁵ - x⁴ + x³ - x² + 1)

\(\left(1+2x\right).\left(1-2x\right)-x.\left(x+2\right).\left(x-2\right)\))

\(=1-\left(2x\right)^2-x.x^2-2^2\)

\(=1-4x^2-x^3-4\)

Ko bt có đúng ko nữa

( 1 + 2x ) ( 1 - 2x ) - x ( x + 2 ) ( x - 2 ) 

= 1 - 4x² - x ( x² - 4 )

= 1 - 4x² - x³ + 4x

= - ( x³ + 4x² - 4x - 1 )

= - ( x³ - x² + 5x² - 5x + x - 1 )

= - [ x² ( x - 1 ) + 5x ( x - 1 ) + ( x - 1 ) ]

= - ( x - 1 ) ( x² + 5x + 1 )

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

hc tốt nha !!!!!!!!!

KHÔNG BÍT

\(x^5+x+1=x^5-x^2+x^2+x+1=x^2\left(x^3-1\right)+\left(x^2+x+1\right)\)

\(=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)

ta có : x^8 +x^4 +1= (x^8 -x^5) +(x^5-x^2) +(x^4 -x) +(x^2 +x 1)=x^5.(x^3 -1) +x^2(x^3-1) +x(x^3-1) +(x^2 +x+1)=x^5.(x-1)(x^2 +x+1) +x^2(x-1)(x^2 +x+1) +x(x-1)(x^2 +x+1) +(x^2 +x+10=(x^2 +x+1)(x^6- x^5 +x^3 -x +1)

\(x^2+x-1\)=\(x^2+2x\frac{1}{2}+\frac{1}{4}-\frac{5}{4}\)=\(\left(x+\frac{1}{2}\right)^2-\left(\frac{\sqrt{5}}{2}\right)^2\)=\(\left(x+\frac{1}{2}-\frac{\sqrt{5}}{2}\right)\left(x+\frac{1}{2}+\frac{\sqrt{5}}{2}\right)\)

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

Đặt x^2+2x+1=y ta được:

(y-)(y+1)+1=y^2-1+1=y^2

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

= ( x + 1 )^4