Question

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)?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

\[=(x+1/2)(2(x^2+x+1)q(x)+4x+2))+3\]

Answer 7

q(x)=(x-1)t(x)

As a start, plugin x = 1 above

Answer 8

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)

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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