The polynomial leaves a remainder of when divided by and a remainder of when divided by .

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The polynomial

g(x)=x^{4}-5x^{3}+6x^{2}+px+q

leaves a remainder of

4

when divided by

(x-1)

and a remainder of

-2

when divided by

(x-2)

. (i) Form two equations in

p

and

q

using the given information and hence find the values of

p

and

q

. (ii) With the values of

p

and

q

found in part (i), calculate the remainder when

g(x)

is divided by

(x-3)

. (iii) For what value of

x

will the remainder obtained in part (ii) become zero? Explain your answer briefly.