SOLUTION: If polynomial {{{4x^3y-m}}} has factorization {{{4xy(x^2-y^2+ab)}}}, what is the value of m?

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Question 888733: If polynomial 4x%5E3y-m has factorization 4xy%28x%5E2-y%5E2%2Bab%29, what is the value of m?
Found 2 solutions by Edwin McCravy, josgarithmetic:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
If polynomial 4x%5E3y-m has factorization 4xy%28x%5E2-y%5E2%2Bab%29,
what is the value of m?
4x%5E3y-m =

4xy%28x%5E2-m%2F%284xy%29%29 which must be identical with  4xy%28x%5E2-y%5E2%2Bab%29, 

Therefore -y%5E2%2Bab%22%22=%22%22-m%2F%284xy%29

          %28-4xy%29%28-y%5E2%2Bab%29%22%22=%22%22m

          4xy%5E3-4abxy%22%22=%22%22m

Edwin

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E3y-m divided by 4xy%28x%5E2-y%5E2%2Bab%29 would have remainder equaling 0. Do the polynomial division first. Equate the remainder to zero and solve for m.

McCravey already did the work and found an expression for m, which is better.