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Factorise the expression using a suitable method and choose the option which represents the factored form of $x 3 − 3 x 2 + x − 3$ .

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(x 2 + 1) (x − 3)

(x 2 − 1) (x − 3)

(x 2 + 3) (x − 1)

(x 2 − 3) (x + 1)

answer is A.

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Detailed Solution

We are given a polynomial expression as follows,

x 3 − 3 x 2 + x − 3

.
Now, it can be observed that there are four terms in the expression. So, we proceed by regrouping the terms with the common factors as follows,

(x 3 − 3 x 2) + (x − 3)

Now, we will factor out the common terms from the above regrouped expression as follows,

x 2 x − 3 + x − 3 = x 2 x − 3 + 1 x − 3 = x − 3 x 2 + 1

Rearranging the above expression, we have

(x 2 + 1) (x − 3)

as the factored form of the expression

x 3 − 3 x 2 + x − 3

.
Hence, the correct option is (1).

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