Solve for x x^4-2x^3-x^2+2x=0

Problem

x4−2*x3−x2+2*x=0

Solution

1. Factor out the greatest common factor, which is x from all terms in the equation.

x*(x3−2*x2−x+2)=0

2. Group the terms inside the parentheses to perform factoring by grouping.

x*((x3−2*x2)−(x−2))=0

3. Factor out the common binomial from each group.

x*(x2*(x−2)−1*(x−2))=0

4. Extract the common factor (x−2) from the expression.

x*(x−2)*(x2−1)=0

5. Apply the difference of squares formula to factor (x2−1)

x*(x−2)*(x−1)*(x+1)=0

6. Set each factor to zero using the zero product property to find the individual solutions for x

x=0

x−2=0⇒x=2

x−1=0⇒x=1

x+1=0⇒x=−1

Final Answer

x={0,2,1,−1}

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