Question

Factorise : x3 – 27 – x + 3

Answer 1

Answer:

Let f(x) = x³ + 27

0 = x³ + 27

x³= -27

x = -3

This means that x = -3 is the only zero of the graph of f(x). Since we know

(

x

+

3

)

is one factor of

f

(

x

)

, to find the 2nd factor,

x

3

+

27

x

+

3

We get the second factor to be

x

2

−

3

x

+

9

.

Therefore,

f

(

x

)

=

(

x

+

3

)

(

x

2

−

3

x

+

9

)