A question on polynomials practice question #10 (p. 149 in PWN the SAT Math Guide): I understand how to solve using polynomial long division but can you explain your shortcut from the answer explanation? How would we know to plug in -3?
Sure, here’s the question:

The shortcut in the solution is to plug in , and that comes from the bolded text on page 145 of the book. If you want to know the remainder when a polynomial is divided by
, where
is some constant, then plug
into the polynomial for
and see what comes out. If you get 0, then
is a factor of the polynomial. If you get something other than 0, it’s the remainder.
Since this question is just asking for , the remainder, we can just follow that shortcut. Dividing by
is the same as dividing by
, which is why we plug in
. Does that help?
There’s more on this concept on pages 144 and 145 of the book.
Comments (1)
Yes! Finally grokked it! Thanks, Mike!