Đáp án:
a, Ta có
`x^3 - 5x^2 + 8x - 4`
` = x^3 - x^2 - 4x^2 + 4x + 4x - 4`
` = x^2.(x - 1) - 4x.(x - 1) + 4.(x - 1)`
` = (x - 1)(x^2 - 4x + 4)`
` = (x - 1)(x - 2)^2`
` => (x^3 - 5x^2 + 8x - 4) : (x - 2)`
` = (x - 1)(x - 2)^2 : (x - 2)`
` = (x - 1)(x - 2)`
` = x^2 - x - 2x + 2`
` = x^2 - 3x + 2`
b, Ta có :
Câu b đề sai sửa để `x^3 - 9x^2 + 6x + 16 : (x + 1)`
Ta có :
`x^3 - 9x^2 + 6x + 16`
` = x^3 + x^2 - 10x^2 - 10x + 16x + 16`
` = x^2.(x + 1) - 10x.(x + 1) + 16.(x + 1)`
` = (x + 1)(x^2 - 10x + 16)`
` => x^3 - 9x^2 + 6x + 16 :(x + 1)`
` = (x + 1)(x^2 - 10x + 16) : (x + 1)`
` = x^2 - 10x + 16`
c, Ta có :
`x^3 - 7x + 6`
` = x^3 - x - 6x + 6`
` = x.(x^2 - 1) - 6.(x - 1)`
` = x.(x - 1)(x + 1) - 6(x - 1)`
` = (x - 1)(x^2 + x - 6)`
` = (x - 1)(x^2 - 2x + 3x - 6)`
` = (x + 1)[x.(x - 2) + 3.(x - 2)]`
` = (x + 1)(x - 2)(x + 3)`
` => x^3 - 7x + 6 :(x + 3)`
` = (x + 1)(x - 2)(x + 3) : (x + 3)`
` = (x + 1)(x - 2)`
` = x^2 + x - 2x - 2`
` = x^2 - x - 2`
Giải thích các bước giải: