Coordinate Geometry

Question

Find the remainder when x³ + 3x² + 3x + 1 is divided by

$straight x minus 1 half$

Solution

straight x minus 1 half straight x minus 1 half space equals space space 0 space space space rightwards double arrow space space space space straight x space equals 1 half

therefore space space

Remainder

equals open parentheses 1 half close parentheses cubed plus 3 open parentheses 1 half close parentheses squared plus 3 open parentheses 1 half close parentheses plus 1 equals space 1 over 8 plus 3 over 4 plus 3 over 2 plus 1 space equals space 27 over 8