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

[electrofanner]

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. :)

 

[Mentallic]

To find the value of k you'll need to do polynomial division.

 

[SammyS]

If (a-3b) is a factor of a⁴ - 7a²b² + kb⁴,
then if you plug in 3b for a, you should get zero.

 

[HallsofIvy]

Excellent idea, SammyS!