Factor the following expression.
x2 + 9x + 14
x2 + 9x + 14 =

x = 7

x = 2

Step-by-step explanation:

The first term is,  x2  its coefficient is  1 .

The middle term is,  -9x  its coefficient is  -9 .

The last term, "the constant", is  +14  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 14 = 14  

Step-2 : Find two factors of  14  whose sum equals the coefficient of the middle term, which is   -9 .

     -14    +    -1    =    -15  

     -7    +    -2    =    -9    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  -2  

                    x2 - 7x - 2x - 14

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-7)

             Add up the last 2 terms, pulling out common factors :

                   2 • (x-7)

Step-5 : Add up the four terms of step 4 :

                   (x-2)  •  (x-7)

            Which is the desired factorization