Grades 11-12 Video Solutions 2023-2023_11-12

Video Transcription

Video Summary

The video discusses a problem involving a 5th degree polynomial with integer roots, partially obscured by an inkblot. Using Vieta's formulas, it concludes that the constant term implies the roots' product is 7. Thus, one root must be ±7, and the others ±1. Given the sum of roots is 11 (from the x⁴ coefficient), all roots must be positive: four 1s and one 7. This allows factoring of the polynomial as \((x - 1)^4(x - 7)\). Hence, the highest power of \(x - 1\) dividing the polynomial is 4. The answer is "d".

Keywords

5th degree polynomial

integer roots

Vieta's formulas

factoring polynomial

roots product