Toán phân tich đa thưc thanh nhân tử băng phuong phap đặt an dụ (x+1)(x+3)(x+5)(x+7)+15 07/07/2021 By Brielle phân tich đa thưc thanh nhân tử băng phuong phap đặt an dụ (x+1)(x+3)(x+5)(x+7)+15
$(x+1)(x+3)(x+5)(x+7)+15$ $=[(x+1)(x+7)][(x+3)(x+5)]+15$$=(x^2+8x+7)(x^2+8x+15)+15$Đặt `x^2+8x+11=y` `=(y-4)(y+4)+15` `=y^2-4^2+15` `=y^2-1` `=(y-1)(y+1)` `=(x^2+8x+10)(x^2+8x+12)` Trả lời
Giả sử `A=(x+1)(x+3)(x+5)(x+7)+15` `=(x^2+8x+7)(x^2+8x+15)+15` Đặt `x^2+8x+11=t` `=> A=(t-4)(t+4)+15` `=t^2-16+15` `=t^2-1` `=(t-1)(t+1)` `=(x^2+8x+10)(x^2+8x+12)` `=(x^2+8x+10)(x^2+2x+6x+12)` `=(x^2+8x+10)[x(x+2)+6(x+2)]` `=(x^2+8x+10)(x+2)(x+6)` Trả lời
$(x+1)(x+3)(x+5)(x+7)+15$
$=[(x+1)(x+7)][(x+3)(x+5)]+15$
$=(x^2+8x+7)(x^2+8x+15)+15$
Đặt `x^2+8x+11=y`
`=(y-4)(y+4)+15`
`=y^2-4^2+15`
`=y^2-1`
`=(y-1)(y+1)`
`=(x^2+8x+10)(x^2+8x+12)`
Giả sử `A=(x+1)(x+3)(x+5)(x+7)+15`
`=(x^2+8x+7)(x^2+8x+15)+15`
Đặt `x^2+8x+11=t`
`=> A=(t-4)(t+4)+15`
`=t^2-16+15`
`=t^2-1`
`=(t-1)(t+1)`
`=(x^2+8x+10)(x^2+8x+12)`
`=(x^2+8x+10)(x^2+2x+6x+12)`
`=(x^2+8x+10)[x(x+2)+6(x+2)]`
`=(x^2+8x+10)(x+2)(x+6)`