Question

x-2 divided by 3x^2-5x-22

Answer 1

Factoring  3x2-5x-22 

The first term is,  3x2  its coefficient is  3 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  -22 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -22 = -66 

Step-2 : Find two factors of  -66  whose sum equals the coefficient of the middle term, which is   -5 .

     -66   +   1   =   -65     -33   +   2   =   -31     -22   +   3   =   -19     -11   +   6   =   -5   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -11  and  6 

                     3x2 - 11x + 6x - 22

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

                    x • (3x-11)

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

                    2 • (3x-11)

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

                    (x+2)  •  (3x-11)

             Which is the desired factorization

Thus the answer is 0