Factor 6x^2-7x+2

Problem

6*x2−7*x+2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=−7 and c=2

2. Find two numbers that multiply to a⋅c=12 and add to b=−7

3. Determine the two numbers, which are −3 and −4 since (−3)*(−4)=12 and −3+(−4)=−7

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

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

6. Factor out the common binomial (2*x−1) to obtain the final factored form.

Final Answer

6*x2−7*x+2=(3*x−2)*(2*x−1)

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