`33)`
`x^2 - x - 6`
`= x^2 - 3x + 2x - 6`
` = x (x-3) + 2 (x-3) `
`= (x+2)(x-3)`
`34)`
`x^4 + 4x^2 - 5`
` = (x^4 + 4x^2 + 4) - 9`
`= (x^2 + 2)^2 - 3^2`
`= (x^2 + 2 - 3)(x^2 + 2+ 3)`
` = (x^2 - 1)(x^2+5)`
`=(x-1)(x+1)(x^2+5)`
`35)`
`x^3 - 19x - 30`
` = (x^3 + 5x^2+ 6x) - (5x^2 + 25x + 30)`
` = x (x^2 + 5x + 6) - 5 (x^2 + 5x +6)`
`= (x^2 + 5x + 6)(x-5)`
`= (x^2 + 3x + 2x + 6)(x-5)`
` = [ x (x+3) +2 (x+3)] (x-5)`
` = (x+2)(x+3)(x-5)`
`36)`
`x^4 + x^2 + 1`
`= (x^4 + 2x^2 + 1) - x^2`
`= (x^2 + 1)^2 - x^2`
` = (x^2+ 1 - x^2)(x^2+1+x^2)`
`37)`
Sửa lại đề bài : `(1 + x^2)^2- 4x (1+ x^2)`
` = (1 + x^2)(1 + x^2 - 4x)`
`38)`
`(x^2- 8)^2 + 36`
` = x^4 - 16x^2 + 64 + 36`
` = x^4 - 16x^2 + 100`
`= (x^4 + 20x^2 + 100) - 36x^2`
`= (x^2 + 10)^2 - (6x)^2`
`= (x^2 + 10 - 6x)(x^2 + 10 + 6x)`
`39)`
`81x^4 + 4`
` = (81x^4 + 36x^2+ 4) - 36x^2`
`= (9x^2 + 2)^2 - (6x)^2`
` = (9x^2 + 2 + 6x)(9x^2 + 2 - 6x)`
`40)`
`(x^2 + x)^2 + 4 (x^2 + x) - 12`
` = [ (x^2 +x)^2 + 4 (x^2 + 2) + 4] - 16`
` = (x^2 + x + 2)^2 - 4^2`
`= (x^2+x + 2 - 4)(x^2 + x + 2 + 4)`
` = (x^2 + x -2)(x^2 + x+6)`
` = (x-1)(x+2)(x^2 + x+6)`
`41)`
`(x^2 + x+1)(x^2+x+2) - 12`
`= [ (x^2 + x + 1,5) - 0,5] . [ (x^2 + x + 1,5) + 0,5] - 12`
`= (x^2 + x +1,5)^2 - 0,5^2 - 12`
`= (x^2 + x + 1,5)^2 - 49/4`
`= (x^2 + x + 1,5)^2 - (3,5)^2`
` = (x^2 + x + 1,5 - 3,5)(x^2 + x + 1,5 +3,5)`
` = (x^2 + x - 2)(x^2 + x + 5)`
`= (x-1)(x+2)(x^2+x+5)`
`42)`
`(x^2 + 4x + 8)^2 + 3x (x^2 + 4x + 8) + 2x^2`
` = [ (x^2 + 4x + 8)^2 + 3x (x^2 + 4x + 8) + 9/4x^2) - 1/4x^2`
` = (x^2+ 4x + 8 + 3/2x) - (1/2x)^2`
` = (x^2 + 4x + 8 + 3/2 x + 1/2x)(x^2+ 4x+8+3/2x - 1/2x)`
` = (x^2+ 8 +6x)(x^2 + 8+5x)`
`= (x+4)(x+2)(x^2 + 5x+8)`
`43)`
`(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)-1] . [ (x^2 + 5x+5) + 1] - 24`
`= (x^2 + 5x+5)^2 - 1^2 -24`
`= (x^2+ 5x+5)^2 -25`
` = (x^2 + 5x+5)^2 -5^2`
`= (x^2 +5x+5+5)(x^2+5x+5-5)`
` = (x^2 + 5x + 10)(x^2 +5x)`
`= (x^2+ 5x+10) . (x+5) . x`
`44)`
`2x^3 - 5x^2 + 8x -3`
`= (2x^3 - 4x^2 + 6x) - (x^2 - 2x+3)`
` = 2x (x^2 - 2x+3) - (x^2-2x+3)`
` = (2x-1)(x^2 - 2x+3)`
`45)`
`3x^3 - 14x^2 + 4x +3`
`= (3x^3 - 15x^2 + 9x) + (x^2 - 5x+3)`
` = 3x (x^2 - 5x+3) + (x^2 - 5x+3)`
`= (3x+1)(x^2-5x+3)`
`46)`
`12x^2 + 5x - 12y^2 + 12y - 10xy - 3`
` = (12x^2 + 8xy - 4x) - (12y^2 + 18xy - 6y) + (9x +6y -3)`
` = 4x (3x + 2y - 1) - 6y (3x+ 2y - 1) + 3 (3x + 2y-1)`
`= (4x-6y+3)(3x+2y-1)`
