Algebraic Division

Long Division is a skill which can be transferred to detached co-efficient division in all cases but cannot be substituted by synthetic division for all cases. Synthetic division is used for division by a linear factor only. Division by Inspection can be an option but requires a lot of concentration.

In all cases the expressions must be in strictly descending order of powers. If one is missing you must insert a null term. Eg: 3 x3+4 x−6→3 x3+0x2+4 x−6

3 x3+4 x2−7 x+3÷x+4

Long Division Synthetic Division

3 x2−8 x+25

x+4 ) 3 x3+4 x2−7 x+3 3 4 -7 3

3 x3+12x2 - 4 -12 32 -100

−8 x2−7 x 3 -8 25 -97

−8 x2−32 x

25 x+3

25 x+100

−97 remainder

2 x4+3 x3−4 x2+2 x−8÷ x2+2 x+3

2 x2−1x−8 x

2+2x+3 ) 2 x4+3 x3−4 x2+2 x−8

2 x4+4 x3+6 x2

−1 x3−10x2+2 x

−1 x3−2x2−3 x

−8 x2+5x−8

−8 x2−16 x−24

16 remainder