Factor 5x^2-7x-6

Problem

5*x2−7*x−6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=−7 and c=−6

2. Find two numbers that multiply to a⋅c=5⋅(−6)=−30 and add to b=−7

3. Determine the pair of numbers, which are −10 and 3 since (−10)⋅3=−30 and −10+3=−7

4. Rewrite the middle term −7*x using the two numbers found: 5*x2−10*x+3*x−6

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

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

Final Answer

5*x2−7*x−6=(5*x+3)*(x−2)

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