(Q8) Check in which case the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

t2-3, 2t4+3t3-2t2-9t-12

Given the first polynomial is t2-3

Second polynomial is 2t4+3t3-2t2-9t-12

Let us divide 2t4+3t3-2t2-9t-12 by t2-3 we get

t2+t+
t2-3) t4+t3-t2-t-
t4    -t2
-       +
t3+t2-t-
t3    -t
-       +
t2-
t2-
-   +

Since the remainder is therefore t2-3 is a factor of 2t4+3t3-2t2-9t-12