A factor of a quadratic equation is any number or expression that divides the quadratic equation evenly, leaving no remainder. In simpler terms, if you can express a quadratic equation in the form of a product of two binomials, each binomial is considered a factor of that equation.
For example, take the quadratic equation: x2 – 5x + 6 = 0. This equation can be factored into (x – 2)(x – 3) = 0. Here, both (x – 2) and (x – 3) are factors of the quadratic equation. When we multiply these two binomials back together, we get the original quadratic equation.
Factoring is an essential skill in algebra because it helps solve the quadratic equation by finding its roots or zeros—where the equation equals zero. In this example, the roots are x = 2 and x = 3, which are the values that satisfy the equation. Understanding factors is crucial for simplifying expressions and solving polynomial equations effectively.