Fractorise:
`x ^(3)-3x ^(2) + x-3`

Answer

To factorise the expression \( x^3 - 3x^2 + x - 3 \), we can follow these steps:

### Step 1: Group the terms
We can group the terms in pairs:
\[ (x^3 - 3x^2) + (x - 3) \]

### Step 2: Factor out the common factors from each group
From the first group \( (x^3 - 3x^2) \), we can factor out \( x^2 \):
\[ x^2(x - 3) \]
From the second group \( (x - 3) \), we can factor out \( 1 \):
\[ 1(x - 3) \]

Now, we can rewrite the expression as:
\[ x^2(x - 3) + 1(x - 3) \]

### Step 3: Factor out the common binomial factor
Now we can see that \( (x - 3) \) is a common factor:
\[ (x - 3)(x^2 + 1) \]

### Final Answer
Thus, the factorised form of \( x^3 - 3x^2 + x - 3 \) is:
\[ (x - 3)(x^2 + 1) \]

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