Question

Synthetic Division

(6n^3 - 57n^2 + 69n - 14) ÷ (n - 1/2)

Answer 1

`Lets\ consider\ the\ divisor\ (n-(1)/(2))\ as\ g(x) \\In\ order\ to\ perform\ synthetic\ division\ we\ need\ to\ find\ the\ zero\ of\ the\ divisor\ . \\Hence,\\g(x)=0\\n-(1)/(2)=0\\n= (1)/(2)\\`

`Now\ we\ must\ write\ the\ dividend\ in\ its\ standard\ form\ and\ seperate\ out\ its\ coeffeicient.`
`So,\\\\The\ Coefficients\ will\ be\ in\ this\ order\ : 6,-57,+19,-14`

`(1)/(2)` | 6 -57 19 -14

+ | 3 -27 -4

Q = [6 -54 -8] |-18 =R

`Hence,\\The\ acquired\ quotient\ is\ 6n^2-54n-8`

Hence,

As the divisor is rational,

The quotient would be multiplied by the zero(1/2).

`Hence,\\the\ final\ quotient\ = 3n^2-27n-4`

`Remainder =-9`