Factor 6x^2-5x-6

Problem

6*x2−5*x−6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=−5 and c=−6

2. Find two numbers that multiply to a⋅c=6⋅(−6)=−36 and add to b=−5

3. Determine the pair of numbers, which are −9 and 4 since (−9)⋅4=−36 and −9+4=−5

4. Rewrite the middle term −5*x using the two numbers found: 6*x2−9*x+4*x−6

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)+2*(2*x−3)

6. Factor out the common binomial (2*x−3) to obtain the final factored form.

Final Answer

6*x2−5*x−6=(3*x+2)*(2*x−3)

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