#1**+2 **

This type is a little tricky, RP......

When the divisor is in the linear form ax + b [ or ma + b, in this case ....since "a" is the variable ] we need to be careful about the residual polynomial...the remainder will be correct, however

Set 6a + 8 = 0 ⇒ a = -4/3....this is what we need to divide by

-4/3 [ 6 - 4 - 76 - 44 - 6 - 63 ]

-8 16 80 -48 72

_______________________________

6 -12 - 60 36 -54 9

The correct remainder is 9

Here is where synthetic division fails to produce the correct residual polynomial.....the resulting polynomial * appears * to be :

6a^4 - 12 a^3 - 60a^2 + 36a - 54

However....note that if we performed the "normal" polynomial division....the first term would be......a^4

a^4

6a + 8 [ 6a^5

-(6a^5) ......

So...this means that we need to divide every co-efficient of the apparent residual polynomial by 6 to get the correct answer

So...the residual polynomial is

a^4 - 2a^3 - 10a^2 + 6a - 9 R [ 9/ (6a + 8) ]

Do you see this ??

CPhill
Sep 19, 2018

#2**+1 **

Ah somewhat..still a bit confusing though and I have 4 more of these to do. >.<

RainbowPanda
Sep 19, 2018