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x3 -2x2 + x -1
x
-x+ 5
5x3 -10x2+5x-5
-x4+ 2x3- x2 +x
-x4+7x3-11x2+6x-5
2x^4 - 3x^3 - 3x^2 - 2 + 6x x^2 - 2 2x^2 - 3x + 1 2x^4 -4x^2 -3x^3 + x^2 + 6x - 2 -3x^3 + 6x x^2 - 2 x^2 - 2 0 _ _ _ _ _ _
a) \(x^3-x^2-x+1\)
\(=\left(x^3-x^2\right)-\left(x-1\right)\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-1\right)\)
b) \(x^3-3x+1-3x^2\)
\(=\left(x^3+1\right)-\left(3x^2+3x\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-3x\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
c) \(x^2-4x-5\)
\(=x^2.2x.2+4-9\)
\(=\left(x-2\right)^2-3^2\)
\(=\left(x-2+3\right)\left(x-2-3\right)\)
\(=\left(x+1\right)\left(x-5\right)\)
c) x2 - 4x - 5
= x2-5x+x-5
=(x2-5x)+(x-5)
=x(x-5)+(x-5)
=(x-5)(x+1)
\(A=\left(x^2+3x+1\right)\left(x^2+3x-3\right)-5\)
Đặt \(t=x^2+3x+1\) thì A thành
\(t\left(t-4\right)-5=t^2-4t-5\)
\(t^2-5t+t-5=t\left(t-5\right)+\left(t-5\right)\)
\(=\left(t-5\right)\left(t+1\right)=\left(x^2+3x+1-5\right)\left(x^2+3x+1+1\right)\)
\(=\left(x^2+3x-4\right)\left(x^2+3x+2\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x+2\right)\left(x+4\right)\)
\(a.=x^3-2x^2+x^2-2x+x-2=x^2\left(x-2\right)+x\left(x-2\right)+\left(x-2\right)=\left(x-2\right)\left(x^2+x+2\right)\)
b.\(=2x^3+x^2-2x^2-x-2x-1=x^2\left(2x+1\right)-x\left(2x-1\right)-\left(2x-1\right)\)\(=\left(2x-1\right)\left(x^2-x-1\right)\)
c.\(3x^3-x^2+6x^2-2x-12x+4=x^2\left(3x-1\right)+2x\left(3x-1\right)-4\left(3x-1\right)\)\(=\left(3x-1\right)\left(x^2+2x-4\right)\)
d.\(3x^3-x^2-6x^2+2x+15x-5=x^2\left(3x-1\right)-2x\left(3x-1\right)+5\left(3x-1\right)\)\(=\left(3x-1\right)\left(x^2-2x+5\right)\)
t i c k cho mình nha
x2+3x-5
x
x+3
3x2+9x -15
x3+3x2 -5x
x3+ 6x2+4x-15