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Answer:

option 2 : [tex]=x^4 - 3x^3 +x^2 -4[/tex]

Step-by-step explanation:

Given P(x) = R(x) - C(x)

[tex]R(x) = 2x^4 - 3x^3 + 2x - 1 \ , \ C(x) = x^4 - x^2 + 2x + 3[/tex]

[tex]P(x) = (2x^4 - 3x^3 + 2x -1) - (x^4 -x^2 + 2x +3)[/tex]

      [tex]=2x^4 -3x^3 + 2x -1 -x^4 +x^2 -2x -3[/tex]

      [tex]= (2x^4 - x^4) - 3x^3 +x^2 +(2x -2x) + (-1 -3)[/tex]                [tex][arranging \ terms][/tex]

      [tex]=x^4 - 3x^3 +x^2 -4[/tex]

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