Question

Synthetic method (2m²-3m+10)÷(m-5)

Answer 1

M-5) 2m^2-3m+10 (2m+7
       +2m^2-10m
      (-)        (+)
-----------------------------
                    7m+10
                   +7m-35
                   (-)    (+)
-----------------------------
                           45
----------------------------- 
Step 1: First we have to subtract 2m^2 completely, so I multiplied m-5 with 2m which makes 2m^2-10m
i.e (m-5)(2m)= (m)(2m)+(-5)(2m)= 2m^2-10m
Step 2: Subtract 2m^2-10m from 2m^2-3m, we get 7m as remainder. Brought down 10 to the remainder which makes 7m+10
Step 3: We have to subtract 7m completely, so I multiplied m-5 with 2 which makes 7m-35
i.e (m-5)(7)= 7m-35
Step 4: Subtract 7m-35 from 7m+10, we get 45 as the remainder. The sum stops here as it can't be resolved further.
Check:
(m-5)(2m+7)= (m-5)(2m)+(m-5)(7)= 2m^2-10m+7m-35= 2m^2-3m-35
If we add 45 to the 2m^2-3m-35, we get 2m^2-3m+10
Hope it.