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Find the quadratic polynomial that completes the factorization. \newlinex3−1=(x−1)(_____)x^3 - 1 = (x - 1)(\_\_\_\_\_)

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Factor sums and differences of cubesright chevron icon

Full solution

Q. Find the quadratic polynomial that completes the factorization. \newlinex3−1=(x−1)(_____)x^3 - 1 = (x - 1)(\_\_\_\_\_)
  1. Recognize as Difference of Cubes: To factorize x3−1x^3 - 1, recognize it as a difference of cubes where a=xa = x and b=1b = 1.
  2. Apply Formula: The formula for the difference of cubes is a3−b3=(a−b)(a2+ab+b2)a^3 - b^3 = (a - b)(a^2 + ab + b^2).
  3. Factorize: Apply the formula: (x−1)(x2+x(1)+12)(x - 1)(x^2 + x(1) + 1^2).
  4. Simplify: Simplify the quadratic polynomial: (x−1)(x2+x+1)(x - 1)(x^2 + x + 1).

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