Phân tích thành nhân tử $(3x+2)(3x-5)(x-1)(9x+10)+24x^2$ 15/08/2021 Bởi Jade Phân tích thành nhân tử $(3x+2)(3x-5)(x-1)(9x+10)+24x^2$
`(3x+2)(3x-5)(x-1)(9x+10)+24x^2` `=[(3x+2)(3x-5)][(x-1)(9x+10)]+24x^2` `=(9x^2-15x+6x-10)(9x^2+10x-9x-10)+24x^2` `=(9x^2-9x-10)(9x^2+x-10)+24x^2` $\text{Đặt: $9x^2$ – 10 là: y}$ `⇒(y-9x)(y+x)+24x^2` `=y^2+xy-9xy-9x^2+24x^2` `=y^2-8xy+15x^2` `=y^2-3xy-5xy+15x^2` `=y(y-3x)-5x(y-3x)` `=(y-5x)(y-3x)` $\text{Quay trở lại ta có:}$ `⇒(9x^2-10-5x)(9x^2-10-3x)` Bình luận
Đáp án: Giải thích các bước giải: \(R(x)=(3x+2)(3x-5)(x-1)(9x+10)+24x^2\) \(=[(3x+2)(3x-5)][(x-1)(9x+10)]+24x^2\) \(=(9x^2-9x-10)(9x^2+x-10)+24x^2\) \(=(a-9x)(a+x)+24x^2\) (Đặt \(9x^2-10=a\) ) \(=a^2-8ax+15x^2=(a^2-5ax)-(3ax-15x^2)\) \(=a(a-5x)-3x(a-5x)=(a-3x)(a-5x)\) \(=(9x^2-3x-10)(9x^2-5x-10)\) Bình luận
`(3x+2)(3x-5)(x-1)(9x+10)+24x^2`
`=[(3x+2)(3x-5)][(x-1)(9x+10)]+24x^2`
`=(9x^2-15x+6x-10)(9x^2+10x-9x-10)+24x^2`
`=(9x^2-9x-10)(9x^2+x-10)+24x^2`
$\text{Đặt: $9x^2$ – 10 là: y}$
`⇒(y-9x)(y+x)+24x^2`
`=y^2+xy-9xy-9x^2+24x^2`
`=y^2-8xy+15x^2`
`=y^2-3xy-5xy+15x^2`
`=y(y-3x)-5x(y-3x)`
`=(y-5x)(y-3x)`
$\text{Quay trở lại ta có:}$
`⇒(9x^2-10-5x)(9x^2-10-3x)`
Đáp án:
Giải thích các bước giải:
\(R(x)=(3x+2)(3x-5)(x-1)(9x+10)+24x^2\)
\(=[(3x+2)(3x-5)][(x-1)(9x+10)]+24x^2\)
\(=(9x^2-9x-10)(9x^2+x-10)+24x^2\)
\(=(a-9x)(a+x)+24x^2\)
(Đặt \(9x^2-10=a\) )
\(=a^2-8ax+15x^2=(a^2-5ax)-(3ax-15x^2)\)
\(=a(a-5x)-3x(a-5x)=(a-3x)(a-5x)\)
\(=(9x^2-3x-10)(9x^2-5x-10)\)