Consider the monic cubic polynomial

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

Problem

s(x)=x^{3}+ax^{2}+bx+c

. It satisfies the following conditions:

\;

•

(x+1)

is a factor of

s(x)

\;

•

x=2

is a zero of

s(x)

\;

•

s(1)=10

. (i) Using the three conditions above, set up three equations in

a

b

and

c

. (ii) Solve the system of equations to obtain the values of

a

b

and

c

. (iii) Write

s(x)

in its fully factorised form and list all its zeros.