Factor 3x^2-5x+2

Problem

3*x2−5*x+2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−5 and c=2

2. Find two numbers that multiply to a⋅c=3⋅2=6 and add to b=−5 These numbers are −2 and −3

3. Rewrite the middle term −5*x using the two numbers found: −3*x−2*x

3*x2−3*x−2*x+2

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)−2*(x−1)

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

(3*x−2)*(x−1)

Final Answer

3*x2−5*x+2=(3*x−2)*(x−1)

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