Factor 6x^2-7x-3

Problem

6*x2−7*x−3

Solution

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

2. Find two numbers that multiply to a⋅c=6⋅(−3)=−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 these two numbers as −9*x+2*x

6*x2−9*x+2*x−3

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

3*x*(2*x−3)+1*(2*x−3)

6. Factor out the common binomial (2*x−3)

(3*x+1)*(2*x−3)

Final Answer

6*x2−7*x−3=(3*x+1)*(2*x−3)

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