Question

[shanyuan]

Phân tích các đa thức sau tùng nhân tử:

1. (x²+4x+ 8)²+3x(x²+4x+ 8)+2x²

2.(x-1996)³+(x- 1997)²-1

3. 4(x²+15xx+59)(x²+18x+72)-3x²

Answer 1

[Nobi Nobita]

2. Đặt \(x-1996=t\)

\(\Rightarrow\left(x-1996\right)^3+\left(x-1997\right)^3-1=t^3+\left(t-1\right)^2-1\)

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

\(=t.\left[\left(t^2-t\right)+\left(2t-2\right)\right]=t\left[t\left(t-1\right)+2\left(t-1\right)\right]\)

\(=t\left(t-1\right)\left(t+2\right)=\left(x-1996\right)\left(x-1996-1\right)\left(x-1996+2\right)\)

\(=\left(x-1996\right)\left(x-1997\right)\left(x-1994\right)\)

Answer 2

[l҉o҉n҉g҉ d҉z҉]

1. Đặt x² + 4x + 8 = y

bthuc ⇔ y² + 3xy + 2x²

          = y² + xy + 2xy + 2x²

          = ( xy + y² ) + ( 2x² + 2xy )

          = y( x + y ) + 2x( x + y )

          = ( x + y )( y + 2x )

          = ( x + x² + 4x + 8 )( x² + 4x + 8 + 2x )

          = ( x² + 5x + 8 )( x² + 6x + 8 )

          = ( x² + 5x + 8 )( x² + 2x + 4x + 8 )

          = ( x² + 5x + 8 )[ x( x + 2 ) + 4( x + 2 ) ]

          = ( x² + 5x + 8 )( x + 2 )( x + 4 )

2. Đặt t = x - 1996 

bthuc ⇔ t³ + ( t - 1 )² - 1

           = t³ + t² - 2t + 1 - 1

           = t³ + t² - 2t

           = t( t² + t - 2 )

           = t( t² - t + 2t - 2 )

           = t( t - 1 )( t + 2 )

           = ( x - 1996 )( x - 1996 - 1 )( x - 1996 + 2 )

           = ( x - 1996 )( x - 1997 )( x - 1994 )

3. 4( x² + 15x + 59 )( x² + 18x + 72 ) - 3x² < bó tay :)) >