#1**+10 **

45x^5+6x^4+3x^3+8x+12 by 3x-12

This is certainly an unusual one!!!!

First, we want to factor the denominator as 3[x - 4]

Then, we want to divide all the coefficients by 3 [don't forget to include the "missing" power of x^2....it's coefficient will be 0

[45x^5 + 6x^4 + 3x^3 + 0x^2 + 8x + 12] / [3 (x - 4)] =

This results in :

[15x^5 + 2x^4 + x^3 + 0x^2 + (8/3)x + 4] / (x - 4)

Now, proceed normally

4 [ 15 2 1 0 8/3 4 ]

60 248 996 3984 47840/3

--------------------------------------------------------------

15 62 249 996 11960/3 47852/3

And the resultant polynomial is :

15x^4 + 62x^3 + 249x^2 + 996x + 11960/3 + remainder of 47852 / 3

CPhill
Jan 8, 2016

#1**+10 **

Best Answer

45x^5+6x^4+3x^3+8x+12 by 3x-12

This is certainly an unusual one!!!!

First, we want to factor the denominator as 3[x - 4]

Then, we want to divide all the coefficients by 3 [don't forget to include the "missing" power of x^2....it's coefficient will be 0

[45x^5 + 6x^4 + 3x^3 + 0x^2 + 8x + 12] / [3 (x - 4)] =

This results in :

[15x^5 + 2x^4 + x^3 + 0x^2 + (8/3)x + 4] / (x - 4)

Now, proceed normally

4 [ 15 2 1 0 8/3 4 ]

60 248 996 3984 47840/3

--------------------------------------------------------------

15 62 249 996 11960/3 47852/3

And the resultant polynomial is :

15x^4 + 62x^3 + 249x^2 + 996x + 11960/3 + remainder of 47852 / 3

CPhill
Jan 8, 2016

#2**0 **

Hi Chris,

I have used synthaetic division before but if i remember rightly it can only be used when the divisor is a polynomial of degree one.

I can't much see the point of commiting such a limiting proceedure to memory.

I do understand that in this case you were expressely asked to use synthetic division.

Why is this one unusual?

Melody
Jan 8, 2016

#3**0 **

It's unusual - to me - because I don't remember one where we were asked to divide by something in the form of ax + b where "a" was something other than "1"

So....I had to actually factor out the "a" and* divide* the polynomial in the numerator by it before I could perform the synthetic division.....

CPhill
Jan 8, 2016