Dear Student,

$2{x}^{2}-3x-5$ can be the factor of $10{x}^{4}-29{x}^{3}+29x-10$ only when on division the remainder must be ZERO.

Thus, dividing $10{x}^{4}-29{x}^{3}+29x-10$ by $2{x}^{2}-3x-5$, we get,

Since, on division, the remainder is ZERO, hence we can say that $2{x}^{2}-3x-5$ is a factor of $10{x}^{4}-29{x}^{3}+29x-10$.

Or, we can also say that