A zero of a function is a number that, when plugged in for the variable, makes the function equal to zero. P ( x ) = 0 As P ( - 1 ) = 0: ( x³ - 3 x² + x + 5 ) : ( x + 1 ) = x² - 4 x + 5 -x³ - x² -------------- - 4 x² + x 4 x²+ 4 x -------------- 5 x + 5 -5 x - 5 ------------ 0 The remaining trinomial: x² - 4 x + 5 doesn´t have rational roots. Answer: x = -1
