Bài 5. Phân tích các đa thức sau thành nhân tử:
a) (x²-4x)²-8(x²-4x)+15
b) (x²+2x)²+9x²+18x+20
c) (x+1)(x+2)(x+3)(x+4)-24
d) (x-y+5)-2(x−y+5)+1
Bài 6. Phân

Question

60 d tiep :DDDDDDDDDDDDDDDDD

depzaihocba · Answer

Đáp án:
 
Giải thích các bước giải:
 `5,`
`a, (x^2- 4x)^2- 8(x^2 4x)+15`
`=[ (x^2- 4x)^2- 8(x^2 4x)+16]-1`
`=(x^2- 4x+4)^2- 1`
`=(x^2-4x+5)(x^2- 4x+3)`
`=(x^2- 4x+5)(x-3)(x-1)`
`b, (x^2+ 2x)^2+ 9x^2+ 18x+20`
`=[(x^2+ 2x)^2+ 9(x^2+ 2x)+ 81/4]- 1/4`
`=(x^2+ 2x+ 9/2)^2- 1/4`
`=(x^2+ 2x+4)(x^2+ 2x+5)`
`c, (x+1)(x+2)(x+3)(x+4)-24`
`=(x+1)(x+4)(x+2)(x+3)-24`
`=(x^2+ 5x+4)(x^2+ 5x+6)-24`
`=(x^2+ 5x+5)^2- 1-24`
`=(x^2+ 5x+5)^2- 25`
`=(x^2+ 5x+10)(x^2+ 5x)`
`=(x^2+ 5x+10)x(x+5)`
`d, (x-y+5)^2- 2(x-y+5)+1`
`=(x-y+5-1)^2`
`=(x-y+4)^2`
`6,`
`a, x^2 y+ x^2- y-1`
`=(x^2 y+x^2)-(y+1)`
`=x^2 (y+1)-(y+1)`
`=(x^2- 1)(y+1)`
`=(x-1)(x+1)(y+1)`
`b, (x^2+ x)^2+ 4(x^2+ x)-12`
`=[(x^2+ x)^2+ 4(x^2+ x)+4]-16`
`=(x^2+x+4)^2- 16`
`=(x^2+ x+8)(x^2+x)`
`=(x^2+ x+8)x(x+2)`
`c, (6x+5)^2 (3x+2)(x+1)-6`
`=(36x^2+ 60x+25)(3x^2+ 5x+2)-6`
`=[12(3x^2+ 5x+2)+1](3x^2+ 5x+2)-6`
`=12(3x^2+ 5x+2)^2 +(3x^2+ 5x+2)-6`
`=12(3x^2+ 5x+2)^2- 8(3x^2+ 5x+2)+9(3x^2+ 5x+2)-6`
`=4(3x^2+ 5x+2)[3(3x^2+ 5x+2)-2]+3[3(3x^2+ 5x+2)-2]`
`=[3(3x^2+ 5x+2)-2][4(3x^2+ 5x+2)+3]`
`=(9x^2+ 15x+4)(12x^2+ 20x+11)`
`=(3x+1)(3x+4)(12x^2+ 20x+11)`

224488 · Answer

Bài `5:`
`a) (x^2 -4x )^2 - 8( x^2 - 4x ) + 15`
`= ( x^2 - 4x )^2 - 3( x^2 - 4x)  - 5( x^2 - 4x ) + 15`
`= ( x^2 - 4x - 3 )( x^2 - 4x ) - 5( x^2 - 4x - 3 )`
`= ( x^2 - 4x - 3 )( x^2 - 4x - 5 )`
`= ( x^2 - 4x - 3 )( x^2 - 5x + x - 5 )`
`= ( x - 5 )( x + 1 )( x^2 - 4x -3 )`
`b) ( x^2 + 2x )^2 + 9x^2 + 18x + 20`
`= ( x^2 + 2x )^2 + 9( x^2 +2x ) + 20`
`= (x^2 + 2x )^2 + 4(x^2 + 2x ) + 5( x^2+2x ) + 20`
`= ( x^2 + 2x + 4 )( x^2 + 2x ) + 5( x^2 + 2x + 4 )`
`= ( x^2 + 2x + 4 )( x^2 + 2x + 5 )`
`c) ( x + 1 )( x + 2 )( x+ 3 )( x + 4 ) - 24`
`= [ ( x + 1 )( x + 4 ) ][ ( x + 2 )( x + 3 ) ] - 24`
`= ( x^2 + 5x + 4 )( x^2 + 5x + 6 ) - 24`
`= ( x^2 + 5x + 5 )^2 - 1 - 24`
`= ( x^2 + 5x + 5 )^2 - 25`
`= ( x^2 + 5x )( x^2 + 5x + 10 )`
`= x( x + 5 )(x^2 + 5x + 10 )`
`d) ( x - y + 5 )^2 - 2(x - y + 5 ) + 1`
`= ( x - y + 5 - 1 )^2`
`= ( x - y + 4 )^2`
Bài `6:`
`a) x^2y + x^2 - y - 1`
`= x^2( y + 1 ) - ( y + 1 )`
`= ( y + 1 )( x^2 - 1 )`
`= ( y + 1 )( x - 1 )( x + 1 )`
`b) ( x^2 + x )^2 + 4( x^2 + x ) - 12`
`= ( x^2 + x ) - 2( x^2 + x ) + 6( x^2 + x ) - 12`
`= ( x^2 + x )( x^2 + x -2 ) + 6( x^2 + x - 2 )`
`= ( x^2 + x - 2 )( x^2 + x + 6 )`
`= ( x^2 - x + 2x - 2 )( x^2 + x+ 6 )`
`= ( x - 1 )( x + 2 )( x^2 + x + 6 )`
`c) ( 6x + 5 )^2( 3x + 2 )( x + 1 ) - 6`
`= [( 6x + 5 )^2( 3x + 2 )( 12x + 12 ) - 72 ]/12`
`= (( 36x^2 + 60x + 25 )( 36x^2 + 60x + 24 ) - 72 ]/12`
`= (( 36x^2 + 60x + 24 )^2 + ( 36x^2 + 60x + 24 ) - 72 ]/12`
`= (( 36x^2 + 60x + 24 )^2 - 8( 36x^2 + 60x + 24 ) + 9( 36x^2 + 60x + 24 ) - 72 ]/12`
`= 1/12[( 36x^2 + 60x + 24 )( 36x^2 + 60x + 16 ) + 9( 36x^2 + 60x + 16 ) ]`
`= 1/12( 36x^2 + 60x + 33 )( 36x^2 + 60x + 16 )`
`= ( 12x^2 + 20x + 11 )( 9x^2 + 15x + 4 )`
`= ( 12x^2 + 20x + 11 )( 9x^2 + 12x + 3x + 4 )`
`= ( 12x^2 + 20x + 11 )( 3x + 4 )( 3x + 1 )`

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