Could you further explain your explanation of Practice Question #4 in PWN the SAT Math Guide “Polynomials” chapter (p. 148). In your long division confirmation of the answer (explanation p. 326), how do you know to divide by 9x + 1?
Sure. Here’s the question:
First, as I say in the solution, all you really need to do here is pay attention to the leading terms. When you divide 
by 
and get 
, then 
must be 9.
When I check by doing long division, I use 
because I’m trying to confirm that the equation works if 
. As shown in the solution, the long division of 
works out to 
with a remainder of 5—or 
. That matches the right hand side of the original equation.