Grades 11-12 Video Solutions 2024-2024_11-12

Video Transcription

Video Summary

The polynomial \( p(x) \) satisfies the condition \( p(x + 1) = x^2 - x + 2p(6) \) for all real \( x \). By substituting \( x = 5 \), we find \( p(6) = -20 \). Substituting back, we get \( p(x + 1) = x^2 - x - 40 \). The sum of the coefficients of \( p(x) \) is determined by evaluating \( p(1) \), which equals \( p(0 + 1) = 0^2 - 0 - 40 \), giving a sum of \(-40\). Thus, the sum of the coefficients of \( p \) is \(-40\).

Keywords

polynomial

coefficients

substitution

evaluation

sum