Important Relationships

We emphasize the important relationships among the following concepts.

• the x-intercepts of the graph of y = f(x)
• the zeros of the function f
• the solutions of the equation f(x) = 0
• the factors of f(x)

Relationships among x-Intercepts, Zeros, Solutions, and Factors

If f is a polynomial function and a is an x-intercept of the graph of then a is a zero of f, a is a solution of f(x) = 0, and x − a is a factor of f(x).