Question

trying to help my son here can someone help?

6x^4+2x³-6x²-14x-1 ÷3x+1

we got 2x³-2x-4 3/3x+1 R

I can't write all the steps out on here because it would take forever...I just want to know if this is what anyone else gets and if not can you help us? Just need to know if we are working this correctly or not...


also i would guess that being that there is a Remainder then this is not a factor?

Answer 1

First what I did was try to factor out the bottom using synthetic division and got a remainder as well, so no 3x + 1 is not a factor.
I tried to factor the numerator, but came up empty so I plugged it into my calculator for the factors and the numerator has no roots that are integers :(

I tried to keep working on it on paper, but there were no factors that are integers :(
I hope I helped you some :|

Answer 2

OK, so you'll need to try taking 3x+1 from two at a time.

6x^4 + 2x^3 = (2x^3)*(3x+1)

THEN

-6x^2 -2x = (-2x)*(3x+1)

THEN

-12x - 1 = (-4)*(3x+1)

So, you get (3x+1)*(2x^3-2x-4)

Cancel the 3x+1 from top and bottom and get:

2x^3 - 2x - 4

Hope that made sense!