A cubic polynomial satisfies the following conditions: • is a factor of , • is a…

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

Problem

A cubic polynomial

f(x)=ax^{3}+bx^{2}+cx-6

satisfies the following conditions: •

(x-1)

is a factor of

f(x)

, •

(x-3)

is a factor of

f(x)

, • when

f(x)

is divided by

x+2

, the remainder is

30

. (i) Form three equations in

a

b

and

c

based on the above information. (ii) Solve the system of equations to find the values of

a

b

and

c

. (iii) Using the values of

a

b

and

c

, factorise

f(x)

completely.