POLYNOMIALS
posted by Aoi
I'm really sorry, i'm preparing for O levels, so i have a lot of maths questions to ask... please excuse me...
Question:
Find the value of k for which a3b is a factor of a^4  7a^2b^2 + kb^4. Hence, factorise completely.
How do i even find k???
Please help thankyou!

Reiny
Using either long division or by synthetic division I go
(a^4  7a^2b^2 + kb^4)÷ (a3b) = a^3 + 3a^2b  7ab^2 + 21b^3 with a remainder of 63k^4 + kb^4
but there was to be no remainder, so
63k^4 + kb^4 = 0
k = 63
so a^3 + 3a^2b  7ab^2 + 21b^3 = 0
use grouping
a^2(a+3b) + 7b^2(a+3b) = 0
(a+3b)(a^2 + 7b) = 0
so the original factors to
(a3b)(a+3b)(a^2 + 7b)
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