Rethwrit
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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)