Factorise:
$3x^{3}-x^{2}-3x+1$
$3x^{3}-x^{2}-3x+1$
(D) Let $f(x) = 3x^{3}-x^{2}-3x+1$ be the given polynomial.
We can factorize this by grouping terms:
$f(x) = (3x^{3}-3x) - (x^{2}-1)$
$f(x) = 3x(x^{2}-1) - 1(x^{2}-1)$
$f(x) = (3x-1)(x^{2}-1)$
Since $x^{2}-1$ is a difference of squares,we can write it as $(x-1)(x+1)$.
Therefore,$f(x) = (3x-1)(x-1)(x+1)$.
We can factorize this by grouping terms:
$f(x) = (3x^{3}-3x) - (x^{2}-1)$
$f(x) = 3x(x^{2}-1) - 1(x^{2}-1)$
$f(x) = (3x-1)(x^{2}-1)$
Since $x^{2}-1$ is a difference of squares,we can write it as $(x-1)(x+1)$.
Therefore,$f(x) = (3x-1)(x-1)(x+1)$.
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