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Write a polynomial of least degree with roots 77, 7-7, and 2-2. Write your answer using the variable xx and in standard form with a leading coefficient of 11.

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Q. Write a polynomial of least degree with roots 77, 7-7, and 2-2. Write your answer using the variable xx and in standard form with a leading coefficient of 11.
  1. Identify factors for roots: Identify the linear factors for each root: for root 77, the factor is (x7)(x - 7); for root 7-7, the factor is (x+7)(x + 7); for root 2-2, the factor is (x+2)(x + 2).
  2. Multiply factors for polynomial: Multiply these factors to get the polynomial: (x7)(x+7)(x+2)(x - 7)(x + 7)(x + 2).
  3. Simplify first two factors: Simplify the first two factors: (x7)(x+7)=x249(x - 7)(x + 7) = x^2 - 49.
  4. Multiply simplified factors: Now multiply (x249)(x^2 - 49) by (x+2)(x + 2): (x249)(x+2)=x3+2x249x98(x^2 - 49)(x + 2) = x^3 + 2x^2 - 49x - 98.

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