@butterflylemon You’re never required to use synthetic division since you could just use polynomial long division.
Someone else could correct me if I’m wrong (as it’s been 4+ years since I’ve taken the SAT/ACT), but I don’t recall ever having to do polynomial long division on the SAT or ACT. One reason is probably because dividing polynomials takes a bit of time. Another reason is there is usually a simpler approach for a given question.
This is not an SAT or ACT question, but suppose you were asked to find the product of the roots of the polynomial x^3 + 9x^2 + 14x - 24. You could notice that 1 is a root, then divide by x-1 to yield a quadratic, then find the roots of the quadratic. But why waste time doing that?