Answer 1

To simplify, we will proceed as follows:

\[\left( x^3 - 2 x^2 + 5x - 7 \right)\left( 2x - 3 \right)\]

\[ = 2x\left( x^3 - 2 x^2 + 5x - 7 \right) - 3\left( x^3 - 2 x^2 + 5x - 7 \right)\]

\[ = 2 x^4 - 4 x^3 + 10 x^2 - 14x - 3 x^3 + 6 x^2 - 15x + 21\]

\[= 2 x^4 - 4 x^3 - 3 x^3 + 10 x^2 + 6 x^2 - 14x - 15x + 21\]   (Rearranging)

\[= 2 x^4 - 7 x^3 + 16 x^2 - 29x + 21\]   (Combining like terms)
Thus, the answer is \[2 x^4 - 7 x^3 + 16 x^2 - 29x + 21\].