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x â a is a factor of the polynomial f(x) if f(a) = 0. The Factor Theorem. If f(x) is a polynomial and f(p) = 0 then (x â p) is a factor of f(x). If f(x) is a polynomial and f(âq) = 0 then (x + q) is a factor of f(x). Polynomials-Factor Theorem. Description and examples of the Factor Theorem. Prove that (x + 1) is a factor of P(x) = x 2 + 2x + 1.
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.