(Q10) Check in which case the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial
x3-3x+1, x5-4x3+x2+3x+1
Answer
Given first polynomial x3-3x+1,
Second polynomial x5-4x3+x2+3x+1
Let us divide x5-4x3+x2+3x+1
by x3-3x+1, we get
2-
x3-3x+1)5-x3+2+x+
5-x3+2
- + -
-3+x+
-3+x-
+ - +
+
Here remainder is (≠0)
Therefore x3-3x+1 is not a factor of x5-4x3+x2+3x+1