Factorization of polynomial ( a &#x2212;<!-- − --> b ) 4 </msup> + ( b

Brooklynn Hubbard

Brooklynn Hubbard

Answered question

2022-05-12

Factorization of polynomial ( a b ) 4 + ( b c ) 4 + ( c a ) 4

Answer & Explanation

Darion Sexton

Darion Sexton

Beginner2022-05-13Added 14 answers

Let x = a b and y = b c then a c = x + y so we have
. . . = x 4 + y 4 + ( x + y ) 4 = 2 x 4 + 4 x 3 y + 6 x 2 y 2 + 4 y 3 x + 2 y 4 = 2 ( x 4 + 2 x 3 y + 3 x 2 y 2 + 2 y 3 x + y 4 ) = 2 ( x 2 + x y + y 2 ) 2
In general:
If f ( x , y ) is 4 degree polynomial then you can try factor it by setting
f ( x , y ) = ( a x 2 + b x y + c y 2 ) ( d x 2 + e x y + f y 2 )
or
f ( x , y ) = ( a x + b y ) ( c x 3 + d x 2 y + e x y 2 + f y 3 )
Now all you have to find are those coefficents.

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