Đáp án+Giải thích các bước giải:
`a)x^4+2x^2-3`
`=x^4+3x^2-x^2-3`
`=x^2(x^2+3)-(x^2+3)`
`=(x^2+3)(x^2-1)`
`=(x-1)(x+1)(x^2+3)`
`b)(2x+1)^4-3(2x+1)^2+2`
`=(2x+1)^4-(2x+1)^2-2(2x+1)^2+2`
`=(2x+1)^2[(2x+1)^2-1]-2[(2x+1)^2-1]`
`=[(2x+1)^2-1][(2x+1)^2-2]`
`=(2x+1+1)(2x+1-1)(4x^2+4x+1-2)`
`=2x(2x+2)(4x^2+4x-1)`
`=4x(x+1)(4x^2+4x-1)`
`c)x(x+1)(x+2)(x+3)-24`
`=[x(x+3)][(x+1)(x+2)]-24`
`=(x^2+3x)(x^2+3x+2)-24`
`=(x^2+3x+1)^2-25`
`=(x^2+3x+1-5)(x^2+3x+1+5)`
`=(x^2+3x-4)(x^2+3x+6)`
`=(x^2-x+4x-4)(x^2+3x+6)`
`=[x(x-1)+4(x-1)](x^2+3x+6)`
`=(x-1)(x+4)(x^2+3x+6)`
`d)(x+1)(x+2)(x+4)(x+5)-4`
`=[(x+1)(x+5)][(x+2)(x+4)]-4`
`=(x^2+6x+5)(x^2+6x+8)-4`
`=(x^2+6x+5)^2+3(x^2+6x+5)-4`
`=(x^2+6x+5)^2-(x^2+6x+5)+4(x^2+6x+5)-4`
`=(x^2+6x+5)(x^2+6x+5-1)+4(x^2+6x+5-1)`
`=(x^2+6x+4)(x^2+6x+9)`
`=(x+3)(x^2+6x+4)`
