Thread: Long Division of Functions to find Factors

I'm taking an online course and this weeks lesson is long division of functions. The text has no explanation on how to do it, so any help would be appreciated.

For the function

f(x) = x^4 – 3x^3 + x^2 + 3x + 702

use long division to determine whether x+6 is a factor of f(x)

I have no idea where to start... thanks!

Originally Posted by amandagarcia0709

I'm taking an online course and this weeks lesson is long division of functions. The text has no explanation on how to do it, so any help would be appreciated.

For the function

f(x) = x^4 – 3x^3 + x^2 + 3x + 702

use long division to determine whether x+6 is a factor of f(x)

I have no idea where to start... thanks!

do the long division ...

Code:

.......x^3 - 9x^2 + 55x - 327 
-----------------------------------
x+6 | x^4 - 3x^3 + x^2 + 3x + 702
......x^4 + 6x^3
-----------------------------------
...........-9x^3 + x^2 + 3x + 702
...........-9x^3 - 54x^2 
-----------------------------------
..................55x^2 + 3x + 702
..................55x^2 + 330x
------------------------------------
.........................-327x + 702
.........................-327x - 1962
---------------------------------------
.................................2664

since you get a remainder, (x+6) is not a factor.


btw, here is a much easier method ...

if f(-6) = 0 , then (x+6) is a factor

Actually, I don't understand how to do the long divison...can you explain that?

Sorry for the confusion...

Originally Posted by amandagarcia0709

Actually, I don't understand how to do the long divison...can you explain that?

Sorry for the confusion...

go to the link ...

Polynomial Long Division