Question

When the function g(x) is divided by (x-3) and (x-2), the remainder is -10 and -8 respectively. Find the remainder when g(x) is divided by (x^2 - 5x + 6)

Answer 1

See Question 2c of this exam. It's very similar.

Answer 2

http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2010exams/pdf_doc/2010-hsc-exam-mathematics-extension-1.pdf

Answer 3

and the solution : http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2010exams/pdf_doc/mathematics-ext1-sample-answers-10.pdf

Answer 4

Let P(x)= (x-3)(x-2) Q(x) +ax+b

Answer 5

P(3)=-10 ---> 3a+b =-10

P(2)= -8 --> 2a+b =-8

Answer 6

First equation minus second equation

a= -2
b=-8-2(-2) = -8+4 =-4

Answer 7

So the answer is -2x-4