f(x) is a polynomial equation. f(x)=(2x+1)q(x)+4, q(x)=(x-1)t(x). If (x^2+x+1)f(x)=(x+1/2)g(x)+R(x), what is g(1)?

Question

anonymous · Answer

I got 3 as an answer but the answer booklet says 6

anonymous · Answer

Can you show your work, I may be able to point out your error, If you have one.

anonymous · Answer

also, is R(x) defined by an equation?

anonymous · Answer

Sure
$$f(x)=(2x+1)q(x)+4, q(x)=(x-1)t(x)$$
$$(x^2+x+1)f(x)=(x^2+x+1)(2x+1)q(x)+4(x^2+x+1)=2(x^2+x+1)(x+1/2)q(x)+4(x^2+x+1)$$

anonymous · Answer

R(x) is not defined
I just set it up just to tell it's a remainder

anonymous · Answer

$$=(x+1/2)(2(x^2+x+1)q(x)+4x+2))+3$$

ganeshie8 · Answer

q(x)=(x-1)t(x)

As a start, plugin x = 1 above

anonymous · Answer

I got that so I got
(x^2+x+1)f(x)=2(x+1/2)(x-1)(x^2+x+1)q'(x)+4(x^2+x+1)

anonymous · Answer

by the way g'(x)=t(x)

anonymous · Answer

so I grouped it with x+1/2 and got the equation above

anonymous · Answer

sorry q'(x) is t(x) mistype

anonymous · Answer

should I just ask my teacher if the answer is wrong?
I've solved it 3 times and with different ways and got the samething