Factor 3x^2-4x+1

Problem

3*x2−4*x+1

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−4 and c=1

2. Find two numbers that multiply to a⋅c=3 and add to b=−4 These numbers are −3 and −1

3. Rewrite the middle term −4*x using the two numbers found: −3*x−x

3*x2−3*x−x+1

4. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

3*x*(x−1)−1*(x−1)

5. Factor out the common binomial (x−1)

(3*x−1)*(x−1)

Final Answer

3*x2−4*x+1=(3*x−1)*(x−1)

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