I need to solve this by using the remainder theorem thing. I don't know the remainder theorem. I tried looking it up but I didn't understand. Are there two different ways to solve using the remainder theorem? Please show work. Sorry. Thank you.

Guest Sep 18, 2019

#3**+3 **

Thanks EP

EP has done it the long way but that is not the remainder theorem.

The remainder theorem might be difficult to understand but it is very simple to use.

The remainder theorem says that if f(x) is divided by (x-k) then the ramainder will be f(k)

in this case k=-4

so the remainder will be

f(-4)

f(-4)=-64+128+6 = 70

The remainder is just the 70 not 70/(x+4)

Simple view

the zero of (x+4) is -4 therefore g(-4) will give the remainder when g(x) is divided by (x+4)

Melody Sep 19, 2019

#4**+2 **

Ooops sorry...... The remainder is of course just 70. If you divide out the entire thing you would have a term of 70/(x+4) i.e.

(x+4) * { x^2 +4x-16 + 70/(x+4) } = x^3 + 8x^2 +6 sorry I took it toooo far !

ElectricPavlov
Sep 19, 2019

#7**0 **

I'm not OP but I do have a similar question to this that I'm stuck on. Do I solve a question like this using what EP used or do I do it like Melody or do I have to do both to find the answer?

Guest Sep 19, 2019