phân tích đt sau thành nt x^4+2018x^2+2017x+2018 17/08/2021 Bởi Gianna phân tích đt sau thành nt x^4+2018x^2+2017x+2018
Đáp án: `(x^2+x+1)(x^2-x+2018)` Giải thích các bước giải: `x^4+2018x^2+2017x+2018` `⇔(x^4-x)+(2018x^2+2018x+2018)` `⇔x(x^3-1)+2018(x^2+x+1)` `⇔x(x-1)(x^2+x+1)+2018(x^2+x+1)` `⇔(x^2+x+1)(x^2-x+2018)` Bình luận
$x^4+2018x^2+2017x+2018$ $=x^4-x+2018x^2+2018x+2018$ $=x(x^3-1)+2018(x^2+x+1)$ $=x(x-1)(x^2+x+1)+2018(x^2+x+1)$ $=(x^2+x+1)(x^2-x+2018$ Bình luận
Đáp án:
`(x^2+x+1)(x^2-x+2018)`
Giải thích các bước giải:
`x^4+2018x^2+2017x+2018`
`⇔(x^4-x)+(2018x^2+2018x+2018)`
`⇔x(x^3-1)+2018(x^2+x+1)`
`⇔x(x-1)(x^2+x+1)+2018(x^2+x+1)`
`⇔(x^2+x+1)(x^2-x+2018)`
$x^4+2018x^2+2017x+2018$
$=x^4-x+2018x^2+2018x+2018$
$=x(x^3-1)+2018(x^2+x+1)$
$=x(x-1)(x^2+x+1)+2018(x^2+x+1)$
$=(x^2+x+1)(x^2-x+2018$