Factor 3x^2-7x+2

Problem

3*x2−7*x+2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−7 and c=2

2. Find two numbers that multiply to a⋅c=3⋅2=6 and add to b=−7

3. Determine the pair of numbers, which are −6 and −1 since (−6)⋅(−1)=6 and (−6)+(−1)=−7

4. Rewrite the middle term −7*x using the two numbers found: 3*x2−6*x−x+2

5. Factor by grouping the first two terms and the last two terms: 3*x*(x−2)−1*(x−2)

6. Factor out the common binomial (x−2) to obtain the final factored form.

Final Answer

3*x2−7*x+2=(3*x−1)*(x−2)

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