What is the difference between a factor of a quadratic equation and a zero of a quadratic equation?

Generally speaking, a factor is the component of a quadratic equation that gives you a zero. For example, if you have the quadratic equation \(x^2 - 4\), you can *factor* it into two parts: \[x^2 - 4 = (x + 2)(x - 2)\] \(x + 2\) and \(x - 2\) are the *factors*, and they give you the two *zeros*, which are 2 and -2. A zero is the value of x at which the parabola that the quadratic formula describes crosses the y axis (i.e., has a value of 0). A factor is a part of the equation. Multiplying all the factors together gives you the original equation.

Shadowfiend is correct, with one small "oops." The zeros are where the curve of the equation crosses the X-axis, not the y-axis. So in the example above, the parabola crosses the x-axis at 2 and -2; it crosses the y-axis at -4. (The constant term of a polynomial is always the y-intercept.)

Hah! Yes indeed, where it crosses the X axis. Thanks for the catch, LBickford :)