Hướng dẫn trả lời:
a) `[15cdot(x - y)^3 + 12cdot(y - x)^2 - x + y] ÷ (3y - 3x)`
`= [15cdot(x - y)^3 + 12cdot(x - y)^2 - (x - y)] ÷ (- 3x + 3y)`
`= (x - y)cdot[15cdot(x - y)^2 + 12cdot(x - y) - 1] ÷ - 3cdot(x - y)`
`= (x - y)cdot[(-3)cdot(-5)cdot(x - y)^2 + (-3)cdot(-4)cdot(x - y) - 3cdot1/3] ÷ - 3cdot(x - y)`
`= - 3cdot(x - y)cdot[-5cdot(x - y)^2 - 4cdot(x - y) + 1/3] ÷ - 3cdot(x - y)`
`= -5cdot(x - y)^2 - 4cdot(x - y) + 1/3`
b) `[5cdot(x - 2y)^4 + (x - 2y)^2 + 2y - x] ÷ (x - 2y)`
`= [5cdot(x - 2y)^4 + (x - 2y)^2 - (x - 2y)] ÷ (x - 2y)`
`= (x - 2y)cdot[5cdot(x - 2y)^3 + (x - 2y) - 1] ÷ (x - 2y)`
`= 5cdot(x - 2y)^3 + (x - 2y) - 1`
c) `[6cdot(x + y)^3 - 5cdot(x + y)^2 + 3cdot(x + y)] ÷ (x + y)`
`= [(x + y)cdot6cdot(x + y)^2 - (x + y)cdot5cdot(x + y) + (x + y)cdot3] ÷ (x + y)`
`= (x + y)cdot[6cdot(x + y)^2 - 5cdot(x + y) + 3] ÷ (x + y)`
`= 6cdot(x + y)^2 - 5cdot(x + y) + 3`
d) `(5x^2 - 3x^3 + 15 - 9x) ÷ (5 - 3x)`
`= [(5x^2 - 3x^3) + (15 - 9x)] ÷ (5 - 3x)`
`= [x^2cdot(5 - 3x) + 3cdot(5 - 3x)] ÷ (5 - 3x)`
`= (x^2 + 3)cdot(5 - 3x) ÷ (5 - 3x)`
`= x^2 + 3`
e) `(-x^2 + 6x^3 - 26x + 21) ÷ (3 - 2x)`
`= (6x^3 - x^2 - 26x + 21) ÷ (- 2x + 3)`
`= [(6x^3 + 8x^2 - 14x) + (- 9x^2 - 12x + 21)] ÷ (- 2x + 3)`
`= [- 2xcdot(-3x^2 - 4x + 7) + 3cdot(-3x^2 - 4x + 7)] ÷ - (2x - 3)`
`= (- 2x + 3)cdot(-3x^2 - 4x + 7) ÷ - (2x - 3)`
`= - (2x - 3)cdot(-3x^2 - 4x + 7) ÷ - (2x - 3)`
`= -3x^2 - 4x + 7`
g) `(x^2 + x^3 - 1 + 5x) ÷ (x - 1)`
Sửa đề: `(x^3 - x^2 + x^5 - 1) ÷ (x - 1)`
`= [(x^5 + x^3) - (x^2 + 1)] ÷ (x - 1)`
`= [x^3cdot(x^2 + 1) - 1cdot(x^2 + 1)] ÷ (x - 1)`
`= (x^3 - 1)cdot(x^2 + 1) ÷ (x - 1)`
`= (x^3 - 1^3)cdot(x^2 + 1) ÷ (x - 1)`
`= (x - 1)cdot(x^2 + xcdot1 + 1^2)cdot(x^2 + 1) ÷ (x - 1)`
`= (x - 1)cdot(x^2 + x + 1)cdot(x^2 + 1) ÷ (x - 1)`
`= (x^2 + x + 1)cdot(x^2 + 1)`
i) Đề sai, mình sẽ sửa nhé!
`(2x^4 + 2x^3 + 3x^2 - 5x - 2x) ÷ (2x^2 + 4x + 7)`
`= (2x^4 + 2x^3 + 3x^2 - 7x) ÷ (2x^2 + 4x + 7)`
`= xcdot(2x^3 + 2x^2 + 3x - 7) ÷ (2x^2 + 4x + 7)`
`= xcdot(2x^3 + 4x^2 - 2x^2 + 7x - 4x - 7) ÷ (2x^2 + 4x + 7)`
`= xcdot[(2x^3 + 4x^2 + 7x) - (2x^2 + 4x + 7)] ÷ (2x^2 + 4x + 7)`
`= xcdot[xcdot(2x^2 + 4x + 7) - 1cdot(2x^2 + 4x + 7)] ÷ (2x^2 + 4x + 7)`
`= xcdot(x - 1)cdot(2x^2 + 4x + 7) ÷ (2x^2 + 4x + 7)`
`= xcdot(x - 1)`
