Degree
SAT glossary · Reading & Writing
Definition
The largest exponent once the polynomial is expanded — readable off a factored form by adding exponents, with no expansion needed (and expanding is where the arithmetic errors live). Two bounds follow and both are tested: a degree-n polynomial has at most n real zeros and at most n-1 turning points, which lets you eliminate options instantly — a graph with four turning points cannot be a cubic.
Degree in plain English
The degree of a polynomial is just the highest power of the variable once everything is fully multiplied out — for example, (x+1)(x+2) has degree 2, since multiplying it out gives you an x^2 term as the highest one. You can actually figure out the degree without expanding anything: just add up the exponents from a factored form, which saves you from doing messy multiplication where arithmetic mistakes love to hide. Once you know the degree n, you get two free facts: the graph can cross the x-axis at most n times, and it can only change direction (turn) at most n-1 times. That means you can instantly rule out answer choices — a graph that turns four separate times could never belong to a cubic (degree-3) function, since a cubic can turn at most twice.
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