(6x^2+19x+7)/(3x+5)

Question

homework question?

Answer 1

Algebraic long division:

           2x +  3         

3x+5 ) 6x²+19x  +7

         - (6x²+10x)

                     9x  +7

                   - (9x+15)

                           -8

Quotient is 2x+3. remainder -8. (2x+3)(3x+5)-8=6x²+19x+7

Synthetic division (divide by factor -5/3):

-5/3 | 6  19 |    7

         6 -10 | -15

         6    9 |  -8 = 6x+9, remainder -8

Quotient is 6x+9, remainder -8.

(6x+9)(x+5/3)-8=(2x+3)(3x+5)-8 explains the apparent discrepancy between the two methods.