Factor 3x^2+5x-12

Problem

3*x2+5*x−12

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=5 and c=−12

2. Multiply the leading coefficient a and the constant term c to find the product a*c

3⋅(−12)=−36

3. Find two numbers that multiply to −36 and add to the middle coefficient b=5

9⋅(−4)=−36

9+(−4)=5

4. Rewrite the middle term 5*x using the two numbers found in the previous step.

3*x2+9*x−4*x−12

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

3*x*(x+3)−4*(x+3)

6. Factor out the common binomial factor (x+3)

(3*x−4)*(x+3)

Final Answer

3*x2+5*x−12=(3*x−4)*(x+3)

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