Factor 3x^2-7x-6

Problem

3*x2−7*x−6

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=3 b=−7 and c=−6

2. Find two numbers that multiply to a⋅c=3⋅(−6)=−18 and add to b=−7

3. Determine the pair of numbers, which are −9 and 2 since (−9)⋅2=−18 and −9+2=−7

4. Rewrite the middle term −7*x using the two numbers found: 3*x2−9*x+2*x−6

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

6. Factor out the common binomial factor (x−3)

Final Answer

3*x2−7*x−6=(3*x+2)*(x−3)

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