Factor 2a^2-a-6

Problem

2*a2−a−6

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=−1 and c=−6

2. Find two numbers that multiply to a*c=2×−6=−12 and add to b=−1

3. Determine that the two numbers are −4 and 3 since (−4)×3=−12 and −4+3=−1

4. Rewrite the middle term −a using these two numbers as −4*a+3*a

5. Group the terms into two pairs: (2*a2−4*a)+(3*a−6)

6. Factor out the greatest common factor from each pair: 2*a*(a−2)+3*(a−2)

7. Factor out the common binomial (a−2) to obtain the final factored form.

Final Answer

2*a2−a−6=(2*a+3)*(a−2)

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