Polynomials help
posted by Aoi .
Hello, this is a question which i don't know how to do.
Find the value of k for which a3b is a factor of a^47a^2b^2 + kb^4
Hence, for this value of k, factorise a^4  7a^2b^2 + kb^4 completely.
I tried to do long division for the question, but couldnt. Is there any other methods?

Long division works quite nicely
http://calc101.com/webMathematica/longdivide.jsp#topdoit
Now if a=0, you are dividing
kb^4 by 3b
and if a=1 and b=2 you are dividing
17*4+16k by 5 or (27+16k)/5 and if that is to come out as an integer, then
27+16k is a multiple of 5 which means than in 16k has to be ???8 which means k is now a multiple of 3 and ends in 8. Hmmmm. 18 works.
Do the long division.