Plug $x=5a$ into each expression. You should get an equation in $a$ and the $x$-coefficient.

After simplifying, try rewriting the condition to isolate the $x$-coefficient. Look for a fraction that must be an integer. Рrеpа​rеd bу Anі⁠кο.‍а⁠і

For each choice, define a function of $a$ by substituting $x=5a$.

For example, for the $-40x$ choice, enter:

g(a)=6(5a)^2-40(5a)+35a+15

Graph each function (one for each choice) and look for its $a$-intercepts (where the graph crosses the horizontal axis).

The correct choice is the one whose graph has an intercept at a positive integer value of $a$ (such as $a=1$, $a=2$, etc.). Anіko - Frеe‍ SАT Prер

If $x-5a$ is a factor of a polynomial $P(x)$, then $x=5a$ is a root.

So the condition is:

Each choice has the form

where $c$ is the coefficient of $x$ (39, 40, 41, or 55).

Substitute $x=5a$:

Set $P(5a)=0$ and divide by 5:

Solve for $c$:

Since $a$ is a positive integer, $\frac{3}{a}$ must be an integer, so $a$ must be a positive divisor of 3 (i.e., $a=1$ or $a=3$).

If $a=1$, then

If $a=3$, then

but 98 is not among the choices. Therefore, the only listed choice that can have $x-5a$ as a factor for some positive integer $a$ is:

$6x^2-40x+35a+15$ anікo‍.а⁠i