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#)Giải :
\(x^3-2x-4\)
\(=x^3+2x^2-2x^2+2x-4x-4\)
\(=x^3+2x^2+2x-2x^2-4x-4\)
\(=x\left(x^2+2x+2\right)-2\left(x^2+2x+2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
\(x^4+2x^3+5x^2+4x-12\)
\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)
\(=x^2\left(x^2+x+6\right)+x\left(x^2+x+6\right)-2\left(x^2+x+6\right)\)
\(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)
Câu 1.
Đoán được nghiệm là 2.Ta giải như sau:
\(x^3-2x-4\)
\(=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) x3-2x2-x+2
=x(x2-1)+2(-x2+1)
=x(x2-1)-2(x2-1)
=(x2-1)(x-2)
b)
x2+6x-y2+9
=x2+6x+9-y2
=(x+3)2-y2
=(x+3-y)(x+3+y)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(x+2\right)\left(x+3\right)\left(2x-5\right)\left(2x-3\right)-90\)
Rút gọn biểu thức,ta được: \(4x^4+4x^3-41x^2-21x\) (cái này bạn tự làm ở nháp)
Ta có: \(4x^4+4x^3-41x^2-21x\)
\(=4x^4-\left(12x^3-16x^3\right)-\left(48x^2-7x^2\right)-21x\)
\(=4x^4-12x^3+16x^3-48x^2+7x^2-21x\)
\(=4x^3\left(x-3\right)+16x^2\left(x-3\right)+7x\left(x-3\right)\)
\(=\left(x-3\right)\left(4x^3+16x^2+7x\right)\)
\(=\left(x-3\right)\left[4x^3+2x^2+14x^2+7x\right]\)
\(=\left(x-3\right)\left[2x\left(2x^2+x\right)+7\left(2x^2+x\right)\right]\)
\(=\left(x-3\right)\left[\left(2x^2+x\right)\left(2x+7\right)\right]\)
\(=\left(x-3\right)x\left(2x+1\right)\left(2x+7\right)\)
Xong chưa nào??
![](https://rs.olm.vn/images/avt/0.png?1311)
x^3+x^2-2x-8
=x3+3x2+4x-2x2-6x-8
=x(x2+3x+4)-2(x2+3x+4)
=(x-2)(x2+3x+4)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) xy+3x-7y-21
=x(y+3)-7(x+3)
=(x-7)(y+3)
b)2xy-15-6x-5y
=2x(y-3)-5(-3+y)
=(2x-5)(y-3)
c)2x^2y+2xy^2-2x-2y
=2x(xy-1)+2y(xy-1)
=(2x+2y)(xy-1)
x(x+3)-5x(x-5)-5(x+3)
=(x-5)(x+3)-5x(x-5)
=(x-5)(x+3-5x)
Câu cuối mình bị nhầm dòng cuối phải là (x-5)(x+3+x-5)=(x-5)(2x-2)nha bạn
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2x^3+x^2-x+3=2x^3+3x^2-2x^2-3x+2x+3=x^2\left(2x+3\right)-x\left(2x+3\right)+2x+3\)
\(=\left(2x+3\right)\left(x^2-x+1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
phân tích đa thức thành nhân tử x^2-(2x+3)(x-5)+3
= -(x-9)(x+2)
nha bạn chúc bạn học tốt ạ
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`2x^2+x-3`
`=2x^2-2x+3x-3`
`=2x(x-1)+3(x-1)`
`=(x-1)(2x+3)`
\(2x^2+x-3\)
\(=2x^2+3x-2x-3\)
\(=\left(2x+3\right)\left(x-1\right)\)