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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:
\(x^3-2x-4\)
\(=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
c. \(x^4-2x^3-2x^2-2x-3=x^3\left(x-3\right)+x^2\left(x-3\right)+x\left(x-3\right)+x-3\)
\(=\left(x-3\right)\left(x^3+x^2+x+1\right)=\left(x-3\right)\left(x+1\right)\left(x^2+1\right)\)
a) \(x^3-2x^2+5x-4\)
\(=x^3-x^2-x^2+x+4x-4\)
\(=x^2\left(x-1\right)-x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-x+4\right)\)
b) \(x^3-x^2+x+3=\left(x+1\right)\left(x^2-2x+3\right)\)
c) \(x^3-6x^2-9x+14=\left(x-7\right)\left(x-1\right)\left(x+2\right)\)
d) \(x^4+2x^2-3=\left(x-1\right)\left(x+1\right)\left(x^2+3\right)\)
a) x3−2x2+5x−4�3−2�2+5�−4
=x3−x2−x2+x+4x−4=�3−�2−�2+�+4�−4
=x2(x−1)−x(x−1)+4(x−1)=�2(�−1)−�(�−1)+4(�−1)
=(x−1)(x2−x+4)
1. ( x2 - x + 2 )4 - 3x2 ( x2 - x + 2 )2 + 2x4
Đặt t = x2 - x + 2 , ta có :
t4 - 3x2t2 + 2x4
= t4 - 2x2t2 - x2t2 + 2x4
= t2 ( t2 - 2x2 ) - x2 ( t2 - 2x2 )
= ( t2 - x2 ) ( t2 - 2x2 )
= ( t - x ) ( t + x ) ( t2 - 2x2 )
= ( x2 - x + 2 - x ) ( x2 - x + 2 + x ) [ ( x2 - x + 2 )2 - 2x2 ]
= ( x2 - 2x + 2 ) ( x2 + 2x ) ( x2 - 3x + 2 ) ( x2 + x + 2 )
2. 3 ( - x2 + 2x + 3 )4 - 26x2 ( - x2 + 2x + 3 )2 - 9x4
Đặt y = - x2 + 2x + 3 , ta có :
3y4 - 26x2y2 - 9x4
= x2y2 + 3y4 - 9x4 - 27x2y2
= y2 ( x2 + 3y2 ) - 9x2 ( x2 + 3y2 )
= ( y2 - 9x2 ) ( x2 + 3y2 )
= ( y - 3x ) ( y + 3x ) ( x2 + 3y2 )
= ( - x2 + 2x + 3 - 3x ) ( - x2 + 2x + 3 + 3x ) [ x2 + 3 ( - x2 + 2x + 3 )2 ]
= ( - x2 - x + 3 ) ( - x2 + 5x + 3 ) ( 3x4 - 12x3 - 5x2 + 36x + 27 )
1, \(x^2-y^2-2x+2y=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x+y-2\right)\left(x-y\right)\)
2, \(x^2-25+y^2+2xy=\left(x+y\right)^2-5^2=\left(x+y-5\right)\left(x+y+5\right)\)
3, \(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)
4, \(x^4+2x^3+x^2=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)
5, \(x^4+8x=x\left(x^3+8\right)=x\left(x+8\right)\left(x^2-8x+64\right)\)
\(1,\)
\(x^2-y^2-2x+2y\)
\(=\left(x^2-y^2\right)-\left(2x-2y\right)\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-2\right)\)
\(2,\)
\(x^2-25+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-25\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
\(3,\)
\(x^2y-x^3-9y+9x\)
\(=\left(x^2y-x^3\right)-\left(9y-9x\right)\)
\(=x^2\left(y-x\right)-9\left(y-x\right)\)
\(=\left(x^2-9\right)\left(y-x\right)\)
\(=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)
\(4,\)
\(x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(5,\)
\(x^4-8x\)
\(=x\left(x^3-8\right)\)
\(=x\left(x-2\right)\left(x^2+2x+4\right)\)
1) \(x^3+2x-3\)
\(=\left(x^3-x^2\right)+\left(x^2-x\right)+\left(3x-3\right)\)
\(=x^2\left(x-1\right)+x\left(x-1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+3\right)\)
2) \(x^3-6x+4\)
\(=\left(x^3-2x^2\right)+\left(2x^2-4x\right)-\left(2x-4\right)\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)-2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x-2\right)\)
3) \(x^3-2x^2+1\)
\(=\left(x^3-x^2\right)-\left(x^2-x\right)-\left(x-1\right)\)
\(=x^2\left(x-1\right)-x\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-x-1\right)\)
4) \(x^3+5x^2-12\)
\(=\left(x^3+2x^2\right)+\left(3x^2+6x\right)-\left(6x+12\right)\)
\(=x^2\left(x+2\right)+3x\left(x+2\right)-6\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2+3x-6\right)\)