Factor x^3-3x^2-x+3

Problem

x^3−3*x^2−x+3

Solution

1. Group the terms into two pairs to prepare for factoring by grouping.

(x^3−3*x^2)+(−x+3)

2. Factor out the greatest common factor from each pair.

x^2*(x−3)−1*(x−3)

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

(x^2−1)*(x−3)

4. Identify the difference of squares in the first factor, as x^2−1 can be written as x^2−1^2

(x−1)*(x+1)*(x−3)

Final Answer

x^3−3*x^2−x+3=(x−1)*(x+1)*(x−3)

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