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Find the quadratic polynomial that completes the factorization. \newliner3+s3=(r+s)(_____)r^3 + s^3 = (r + s)(\_\_\_\_\_)

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Factor sums and differences of cubesright chevron icon

Full solution

Q. Find the quadratic polynomial that completes the factorization. \newliner3+s3=(r+s)(_____)r^3 + s^3 = (r + s)(\_\_\_\_\_)
  1. Identify Sum of Cubes: To factor r3+s3r^3 + s^3, we know it's a sum of cubes which factors as (r+s)(r2−rs+s2)(r + s)(r^2 - rs + s^2).
  2. Factorization Formula: Now, we just need to fill in the quadratic polynomial in the blank.
  3. Complete Factorization: The quadratic polynomial that completes the factorization is r2−rs+s2r^2 - rs + s^2.

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