Question 1106817

P(x)= (x-2)(x-3)Q(x)+ax+b, where Q(x) is the quotient;


Note that '(ax+b)' is the remainder after the division in every case.


P(2)= 2a+b = 4


P(3)= 3a+b = 7


a = 3, b = -2


Let Q(x) = x+c, where c is a constant and also due to the fact that the coefficient of x^3 is 1


P(x)=(x-2)(x-3)(x+c)+3x-2


P(1)= (1-2)(1-3)(1+c)+1=1


2(1+c)=0


c = -1


Q(x)= x-1


P(x) = (x-2)(x-3)(x-1)+3x-2


P(x)= x^3-6x^2+14x-8