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Write a polynomial of least degree with roots 77 and −8-8.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.

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Full solution

Q. Write a polynomial of least degree with roots 77 and −8-8.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.
  1. Find Linear Factor: Find the linear factor for the root 77; the factor is (x−7)(x - 7).
  2. Combine Factors: Find the linear factor for the root −8-8; the factor is (x+8)(x + 8).
  3. Multiply Factors: Combine the factors to form the polynomial: (x−7)(x+8)(x - 7)(x + 8).
  4. Combine Like Terms: Multiply the factors: (x−7)(x+8)=x2+8x−7x−56(x - 7)(x + 8) = x^2 + 8x - 7x - 56.
  5. Combine Like Terms: Multiply the factors: (x−7)(x+8)=x2+8x−7x−56(x - 7)(x + 8) = x^2 + 8x - 7x - 56. Combine like terms: x2+8x−7x−56=x2+x−56x^2 + 8x - 7x - 56 = x^2 + x - 56.

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