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Question

 Which one of the following is a factor of 3\sqrt{3}x^3+2\sqrt{2}x^3-\sqrt{18}xy+6\sqrt{6}
?

  1. \sqrt{3}x+\sqrt{2}y-\sqrt{3}
  2. \sqrt{3}x+\sqrt{2}y-\sqrt{6}
  3. 3x^2+2y^2-\sqrt{18}x-\sqrt{12}y-\sqrt{6}xy+6
  4. 3x^2+2y^2+\sqrt{18}x+\sqrt{12}y-\sqrt{6}xy+6
Answer

‘.’       a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)

3\sqrt{3}x^3+2\sqrt{2}x^3-18xy+6\sqrt{6} =(\sqrt{3}x+\sqrt{2}y+\sqrt{6}) (3x^2+2y^2-\sqrt{18}x-\sqrt{12}y-\sqrt{6}xy+6)

Answer (C)

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