Factor 12x^2+25x+12

Problem

12*x2+25*x+12

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=12 b=25 and c=12

2. Calculate the product of a and c

a*c=12⋅12=144

3. Find two numbers that multiply to 144 and add to the middle coefficient b=25 These numbers are 16 and 9

16⋅9=144

16+9=25

4. Rewrite the middle term 25*x using the two numbers found.

12*x2+16*x+9*x+12

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

(12*x2+16*x)+(9*x+12)

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

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

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

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

Final Answer

12*x2+25*x+12=(3*x+4)*(4*x+3)

Want more problems? Check here!