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

Problem

x^4−3*x^3−x^2+3*x=0

Solution

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

x*(x^3−3*x^2−x+3)=0

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

x*((x^3−3*x^2)−(x−3))=0

3. Factor out common terms from each group, specifically x^2 from the first group and 1 from the second group.

x*(x^2*(x−3)−1*(x−3))=0

4. Factor out the common binomial (x−3) from the expression.

x*(x−3)*(x^2−1)=0

5. Apply the difference of squares formula to factor x^2−1 into (x−1)*(x+1)

x*(x−3)*(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−3=0⇒x=3

x−1=0⇒x=1

x+1=0⇒x=−1

Final Answer

x={−1,0,1,3}

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