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Find the quadratic polynomial that completes the factorization. \newlineq3+r3=(q+r)(_____)q^3 + r^3 = (q + r)(\_\_\_\_\_)

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Full solution

Q. Find the quadratic polynomial that completes the factorization. \newlineq3+r3=(q+r)(_____)q^3 + r^3 = (q + r)(\_\_\_\_\_)
  1. Apply Sum of Cubes Formula: To factor q3+r3q^3 + r^3, we use the sum of cubes formula: a3+b3=(a+b)(a2−ab+b2)a^3 + b^3 = (a + b)(a^2 - ab + b^2).
  2. Identify 'a' and 'b': Let's identify 'a' and 'b' in our expression. Here, a=qa = q and b=rb = r.
  3. Plug in Values: Now, plug in qq and rr into the sum of cubes formula: (q+r)(q2−qr+r2)(q + r)(q^2 - qr + r^2).
  4. Find Quadratic Polynomial: So, the quadratic polynomial that completes the factorization is q2−qr+r2q^2 - qr + r^2.

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