Factor 2x^2+5x-12

Problem

2*x2+5*x−12

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=5 and c=−12

2. Find two numbers that multiply to a⋅c=2⋅−12=−24 and add to b=5

3. Determine the pair of numbers, which are 8 and −3 since 8⋅−3=−24 and 8 + (-3) = 5$.

4. Rewrite the middle term 5*x using the two numbers found: 2*x2+8*x−3*x−12

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

2*x*(x+4)−3*(x+4)

6. Factor out the common binomial (x+4) to obtain the final factored form.

Final Answer

2*x2+5*x−12=(2*x−3)*(x+4)

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