Factor 3x^2-10x+7

Problem

3*x2−10*x+7

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−10 and c=7

2. Find two numbers that multiply to a⋅c=3⋅7=21 and add to b=−10

3. Determine the factors of 21 that satisfy the condition. The numbers −3 and −7 work because (−3)⋅(−7)=21 and −3+(−7)=−10

4. Rewrite the middle term −10*x using the two numbers found:

3*x2−3*x−7*x+7

5. Factor by grouping the first two terms and the last two terms:

(3*x2−3*x)−(7*x−7)

6. Factor out the greatest common factor from each group:

3*x*(x−1)−7*(x−1)

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

(3*x−7)*(x−1)

Final Answer

3*x2−10*x+7=(3*x−7)*(x−1)

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