Math
posted by ABC on .
The quotientire and reminder are x2 and 2x+4 respectively when the polynomial x^33x^2+x+2 is divided by g(x) find g (x).

well, the highest power is 2 to get x2 out of this
(1x^33x^2+1x+2)/(ax^2+bx+c)
=
[ x  2 + (2x+4)/(ax^2+bx+c)]
so multiply
[ x  2 + (2x+4)/(ax^2+bx+c)]
by (ax^2+bx+c)
= 2x+4
2 (ax^2+bx+c)
+x (ax^2+bx+c)
= 42c
2x2bx+cx
2ax^2+bx^2
+ax^3
which has to be x^33x^2+x+2
so
a = 1
3 = 2+b
so
b = 1
1 = 2 2(1)+c
1 = c
so try
g(x) = x^2x+1 
check it
(It works :)