Đáp án:
`b, (x^2 + x)^2 + 4x^2 + 4x - 12`
`= (x^2 + x)^2 + 4(x^2 + x) - 12`
Đặt `x^2 + x = a`, đa thức trở thành:
`a^2 + 4a - 12`
`= a^2 - 2a + 6a - 12`
`= (a^2 - 2a) + (6a - 12)`
`= a(a - 2) + 6(a - 2)`
`= (a - 2)(a + 6)`
`= (x^2 + x - 2)(x^2 + x + 6)`
`= (x^2 - x + 2x - 2)(x^2 + x + 6)`
`= [x(x - 1) + 2(x - 1)](x^2 + x + 6)`
`= (x - 1)(x + 2)(x^2 + x + 6)`
`d, (x + 1)(x + 2)(x + 3)(x +4) + 1`
`=[(x + 1)(x + 4)][(x + 2)(x + 3)] + 1`
`= (x^2 + 4x + x + 4)(x^2 + 3x + 2x + 6) + 1`
`= (x^2 + 5x + 4)(x^2 + 5x + 6) + 1`
Đặt `x^2 + 5x + 5 = a`, ta được:
`(a - 1)(a + 1) + 1`
`= a^2 - 1^2 + 1`
`= a^2`
`= (x^2 + 5x + 5)^2`
`f, (x + 1)(x + 2)(x + 3)(x + 4) - 24`
`=[(x + 1)(x + 4)][(x + 2)(x + 3)] - 24`
`= (x^2 + 4x + x + 4)(x^2 + 3x + 2x + 6) - 24`
`= (x^2 + 5x + 4)(x^2 + 5x + 6) - 24`
Đặt `x^2 + 5x + 5 = a`, ta được:
`(a - 1)(a + 1) - 24`
`= a^2 - 1^2- 24`
`= a^2 - 25`
`= a^2 - 5^2`
`= (a - 5)(a + 5)`
`= (x^2 + 5x + 5 - 5)(x^2 + 5x + 5 + 5)`
`= (x^2 + 5x)(x^2 + 5x + 10)`
`= x(x + 5)(x^2 + 5x + 10)`
