Đáp án:
a, `x^8 + x^7 + 1`
` = x^8 + x^7 - x^6 + x^6 + 1`
`= (x^8 + x^7 + x^6) - (x^6 - 1)`
`= x^6 . (x^2 + x + 1) - (x^3 - 1)(x^3 + 1)`
`= x^6 .(x^2 + x + 1) - (x - 1)(x^2 + x + 1)(x^3 + 1)`
` = x^6 .(x^2 + x + 1) - (x^2 + x + 1)(x^4 - x^3 + x - 1)`
` = (x^2 + x + 1)(x^6 - x^4 + x^3 - x + 1)`
b, `x^3 + 4x^2 - 29x + 24`
` = (x^3 - x^2) + (5x^2 - 5x) - (24x - 24)`
`= x^2 . (x - 1) + 5x . (x - 1) - 24.(x - 1)`
`=(x - 1)(x^2 + 5x - 24)`
`=(x - 1)(x^2 - 3x + 8x - 24)`
`=(x - 1)[x.(x - 3) + 8.(x - 3)]`
`=(x - 1)(x - 3)(x + 8)`
c, `A = (x + 1)(x + 3)(x + 5)(x + 7) + 15`
`= [(x + 1)(x + 7)].[(x + 3)(x + 5)] + 15`
`= (x^2 + x + 7x + 7)(x^2 + 3x + 5x + 15) + 15`
`= (x^2 + 8x + 7)(x^2 + 8x + 15) + 15`
Đặt `t = x^2 + 8x + 11`
`=> A = (t - 4)(t + 4) + 15`
`= t^2 - 16 + 15`
`= t^2 - 1`
`= (t - 1)(t + 1)`
`=> A = (x^2 + 8x + 11 - 1)(x^2 + 8x + 11 + 1)`
`=> A = (x^2 + 8x + 10)(x^2 + 8x + 12)`
d, `x^3 + 6x^2 + 11x + 6`
`= (x^3 + x^2) + (5x^2 + 5x) + (6x + 6)`
`= x^2 . (x + 1) + 5x.(x + 1) + 6.(x + 1)`
`= (x + 1)(x^2 + 5x + 6)`
`= (x + 1)[(x^2 + 2x) + (3x + 6)]`
`=(x + 1)[x.(x + 2) + 3.(x + 2)]`
`=(x + 1)(x + 2)(x + 3)`
Giải thích các bước giải:
