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# System prepended metadata

title: SID6

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According to the Remainder Theorem, the remainder of a polynomial when divided by a linear polynomial of the form $(x - a)$ is equal to the value of the polynomial at $x = a$.

Therefore, to find the remainder when $2x^3 - 3x^2 + 5x - 7$ is divided by $(x - 2)$, we simply need to substitute $x = 2$ into the polynomial. We get:
$$2(2)^3 - 3(2)^2 + 5(2) - 7$$

$$= 16 - 12 + 10 - 7$$

$$= 7$$

Therefore, the remainder when $2x^3 - 3x^2 + 5x - 7$ is divided by $(x - 2)$ is $7$.