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Factor theorem. In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial has a factor if and only if.
DEFINITION. A function f is even if the graph of f is symmetric with respect to the y-axis. Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f. A function f is odd if the graph of f is symmetric with respect to the origin.Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f. 1  Discussion [ Using Flash 2  ]. Examples. 3  An interactive LiveMath notebook to visualize symmetry with respect to the origin.bjectives: In this tutorial, we define what it means for a function to be symmetric with respect to the y-axis and the origin. Algebraic conditions for these two types of symmetry are obtained from the geometrical definitions.