What is the value of k for which (a-3b) is a factor of a4 - 7a2b2 + kb4?

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To determine the value of k for which (a-3b) is a factor of the polynomial a4 - 7a2b2 + kb4, one must perform polynomial division. By substituting a with 3b, the resulting expression should equal zero to confirm that (a-3b) is indeed a factor. The discussion emphasizes the importance of this substitution method for finding k. Participants express a need for assistance in completing the factorization process. Ultimately, the solution hinges on correctly identifying k through these calculations.
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Find the value of k for which (a-3b) is a factor of a4 - 7a2b2 + kb4.

Hence, for this value of k, factorize a4 - 7a2b2 + kb4 completely.

I tried to do it but my mind is not going anywhere.

Any help will be greatly appreciated. :)
 
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To find the value of k you'll need to do polynomial division.
 
If (a-3b) is a factor of a4 - 7a2b2 + kb4,
then if you plug in 3b for a, you should get zero.
 
Excellent idea, SammyS!
 

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