Factor 12x^2+25x+12

Problem

12 x squared plus 25 x plus 12

Solution

1. Identify the coefficients of the quadratic expression in the form a x squared plus b x plus c where a equals 12 b equals 25 and c equals 12

2. Calculate the product of a and c

a c equals 12 times 12 equals 144

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

16 times 9 equals 144

16 plus 9 equals 25

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

12 x squared plus 16 x plus 9 x plus 12

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

open paren 12 x squared plus 16 x close paren plus open paren 9 x plus 12 close paren

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

4 x times open paren 3 x plus 4 close paren plus 3 times open paren 3 x plus 4 close paren

7. Factor out the common binomial factor open paren 3 x plus 4 close paren

open paren 3 x plus 4 close paren times open paren 4 x plus 3 close paren

Final Answer

12 x squared plus 25 x plus 12 equals open paren 3 x plus 4 close paren times open paren 4 x plus 3 close paren

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