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Find the quadratic polynomial that completes the factorization.\newlineq3−125=(q−5)(______)q^3 - 125 = (q - 5)(\_\_\_\_\_\_)

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Full solution

Q. Find the quadratic polynomial that completes the factorization.\newlineq3−125=(q−5)(______)q^3 - 125 = (q - 5)(\_\_\_\_\_\_)
  1. Identifying Difference of Cubes: We know that q3−125q^3 - 125 is a difference of cubes, which factors as (q−5)(q2+5q+25)(q - 5)(q^2 + 5q + 25).
  2. Factoring the Expression: So, the missing quadratic polynomial in the factorization (q−5)(_____)(q - 5)(\_\_\_\_\_) is q2+5q+25q^2 + 5q + 25.

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