Question

find the quadratic polynomial that completes the factorization.\\( v^3 + 125 = (v + 5)(quad) \\)

Explanation:

Step1: Recall sum of cubes formula

The sum of cubes formula is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\). Here, \(a = v\) and \(b = 5\) since \(v^3+125=v^3 + 5^3\).

Step2: Apply the formula

Using the formula \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\) with \(a = v\) and \(b = 5\), we substitute into the formula.
For \(a^2 - ab + b^2\), we get \(v^2-(v\times5)+5^2=v^2 - 5v + 25\).

Answer:

\(v^2 - 5v + 25\)