Polynomials-finding the value of r&g

G

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When rx^3+gx^2+4x+1 is divided by x-1, the remainder is 12. When it is divided by x+3, the remainder is -20. Find the values of r and g.

I did this:
rx^3+gx+4x+1=12
r+g+4+1=12
r+g=12-5
r+g=6
g=6-r


r(-3)^3+g(-3)^2+4(-3)+1=-20
-27r+9g-11=-20
-27r+9g=-9
-27r+9(6-r)=-9
-27r+54-9r=-9
-36r=-63
r=1.75
g=4.25

Cept I did something wrong? cuz the back of the book doesn't match my answers. So can someone show me how to this question properly, thanks a lot.
 
Hello, bittersweet!

A simple (silly) error . . .

When \(\displaystyle rx^3\,+\,gx^2\,+\,4x\,+\,1\) is divided by \(\displaystyle x\,-\,1\), the remainder is \(\displaystyle 12\).
When it is divided by \(\displaystyle x\,+\,3\), the remainder is \(\displaystyle -20\).
Find the values of \(\displaystyle r\) and \(\displaystyle g\).

I did this:

\(\displaystyle rx^3\,+\,gx\,+\,4x\,+\,1\:=\:12\)
\(\displaystyle r\,+\,g\,+\,4\,+\,1\:=\:12\)
\(\displaystyle r\,+\,g\:=\:12\,-\,5\)
\(\displaystyle r\,+\,g\:=\:\)6 <--- here!
Click to expand...
 
Alright, Alright, thanks for pointing out my silly mistake twice :oops: k what did I do wrong this time, its the same type of question:

When x^3+cx+d is divided by x+1, the remainder is 3, and when it is divided by x-2, the remainder is -3. Determine the values of c and d.

-1-1c+d=3
-1c+d=4
d=4+c

2^3+2c+d=-3
8+2c+d=-3
2c+d=-11
2c+4+c=-11
3c=-15
c=-3 d=4+c
d=4-3
d=1

back of the book answers are: c= -14/3, d=-5/3
 
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