Factorize: x² + y – xy – x.

As there is no common factor among all terms, to factorize x² + y – xy – x, we rewrite it by reordering the terms as

⇒ x² + y – xy – x = x² – x + y – xy

We can write x² = x × x, y = (–1) × (–y) and –xy = x × (–y)

⇒ x² + y – xy – x = x × x – x + (–1) × (–y) + x × (–y)

Observe that x is common for the first two terms and – y is common for the next two terms.

⇒ x² – x + y – xy = x(x – 1) + (–y)(–1 + x)

⇒ x² – x + y – xy = x(x – 1) + (–y)(x – 1)

Now, (x – 1) is the common term.

∴ x² + y – xy – x = (x – 1)(x – y)

Hence, the factors of x² + y – xy – x are (x – 1) and (x – y).