SOLUTION: when the polynomial p(x) is divided by (x-2) the remainder is 4 and when p(x) is divided by (x-3), the remainder is 7. And also if p(x) is a cubic function in which x� is unity, q(

Question 1106817: when the polynomial p(x) is divided by (x-2) the remainder is 4 and when p(x) is divided by (x-3), the remainder is 7. And also if p(x) is a cubic function in which x� is unity, q(x) is the quotient when divided by (x-2)(x-3) and p(1)=1. determine q(x) and p(x).
Answer by JThomson(12) (Show Source): You can put this solution on YOUR website!

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

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