Question

Find the quadratic polynomial that completes the factorization. r³-125=(r-5)

Answer 1

The quadratic polynomial that completes the factorization is
`\(r^2 + 5r + 25\).`

Step-by-step explanation:

To find the quadratic polynomial that completes the factorization of
`\(r^3 - 125 = (r - 5)\)` , let's first recognize that
`\(r^3 - 125\)` is the difference of cubes, which can be factored as
`\((r - 5)(r^2 + 5r + 25)\)`. Here, (r - 5) corresponds to the given factor. Now, we need to determine the quadratic factor.

The quadratic factor is obtained by dividing
`\(r^2 + 5r + 25\)` by (r - 5). Performing the division, we get r^² + 5r + 25. This means that r² + 5r + 25 is the quadratic factor we are looking for.

In summary, the quadratic polynomial that completes the factorization is r² + 5r + 25, and this result is derived from recognizing the given cubic expression as a difference of cubes and factoring accordingly. The quadratic factor is then found by dividing the given cubic expression by the known linear factor (r - 5), resulting in r² + 5r + 25.