Question

What is the complete factorization of p(x)=32x5y−2xy5 over the integers?

Answer 1

Answer:

  $p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)$

Step-by-step explanation:

  $p(x)=32x^5y-2xy^5=2xy(16x^4-y^4)=2xy(4x^2-y^2)(4x^2+y^2)\\\\\boxed{p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)}$

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The factoring of the difference of squares is applicable:

  a^2 -b^2 = (a -b)(a +b)