Question

FACTORISE x^3+3x^2+3x+1

Answer 1

Using the rational root theoerm gives...

p=1 & q=-1

All values of +p/q are -1 & 1

(1)^3+3(-1)^2+3(-1) +1

-1+3-3+1=0

therefore x=-1

(1)^3+3(1)^2+3(1) +1

1+3+3+1

=8

therefore not a root at x=1

Divide the polynomial by (x+1)

x^3+3x^3+3x+1/x+1

x^3+x^2+x^2x+x^2x+x+1/x+1

(x^3+x^2) +(x^2+x) +(x^2+x) +(x+1) /x+2

(x^2+x+x+1)

x^2+2x+1

Final answer is (x+1) (x+1) ^2=(x+1) ^3.....

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