The term 20x^{3} appears in both the expressions 20x^{3} + 8x^{2} and 20x^{3} + 10x but factor 20x^{3} in different ways to obtain each polynomial factorization Whether the given statement make sense or does not make sence.

Calculation:
Given that the two expression are $20x^3+8x^2$ and $20x^3+10x$.
In order to factor the expressions $20x^3+8x^2$ and $20x^3+10x$, to find the greatest common factor of both term in given expression and factor out the GCF.
Thus, factor the term $20x^3$ depends on the second term of given expression.
Since the greatest common factor of $20x^3$ and $8x^2$ is $4x^2$, the term $20x^3$ can be written as $5x-4x^2$.
The greatest common factor of $20x^3$ and 10x is 10x, then the term $20x^3$ can be written as $10x\ast 2x^2$.
Therefore, factor $20x^3$ in different ways to obtain each polynomial factorization.
Hence, the statement makes sence.