Factor 6x^2+17x+12

Problem

6*x2+17*x+12

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=17 and c=12

2. Calculate the product a*c by multiplying 6 and 12

a*c=6⋅12=72

3. Find two numbers that multiply to 72 and add to the middle coefficient b=17 These numbers are 8 and 9

8⋅9=72

8+9=17

4. Rewrite the middle term 17*x using the two numbers found in the previous step.

6*x2+8*x+9*x+12

5. Factor by grouping by grouping the first two terms and the last two terms.

(6*x2+8*x)+(9*x+12)

6. Factor out the greatest common factor from each group.

2*x*(3*x+4)+3*(3*x+4)

7. Factor out the common binomial factor (3*x+4)

(3*x+4)*(2*x+3)

Final Answer

6*x2+17*x+12=(3*x+4)*(2*x+3)

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