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x^3-2x^2-x+2=0 , how can I find x?

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1 Answer

Hi again Erlandas;
x3-2x2-x+2=0
Let's factor this equation.
For the FOIL...
FIRST must be (x2)(x)=x3
OUTER and INNER must add-up to -2x2-x
LAST...(2)(1) or (1)(2), and both numbers must be either positive or negative.
(x2-1)(x-2)=0
Let's FOIL...
FIRST...(x2)(x)=x3
OUTER...(x2)(-2)=-2x2
INNER...(-1)(x)=-1x=-x
LAST...(-1)(-2)=2
x3-2x2-x+2=0
So...
(x2-1)(x-2)=0
Either of these parenthetical equations must =0...
x2-1=0
x2=1
x=1 or -1
or...
x-2=0
x=2
 
Let's check our results with the original equation...
x3-2x2-x+2=0
x=1
13-[2(12)]-1+2=0
1-[(2)(1)]-1+2
1-2-1+2
0=0
 
x=2
x3-2x2-x+2=0
23-[2(22)]-2+2
8-[(2)(4)]-2+2
8-8-2+2=0
0=0

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