To find the zeros of a function, all parts of the function must be factored into binomials. A zero is the point at which a function crosses the x-axis.
- Begin breaking down polynomials into binomials
Binomials are two-term expressions such as x + 1, 5x - 3, or 2y + 4. When given a trinomial, determine what factors of the last term add up to make the second term. For example, when given the term x^2 - 6x + 9, the factors of 9 that add up to -6 are -3 and -3. Therefore, this trinomial can be broken into (x - 3)(x - 3).
- Cancel out like terms in the numerator and denominator
If for example the expression x^2 - 6x + 9/x^2 - 2x - 15 is factored, it ends up as (x - 3)(x + 3)/(x - 5)(x + 3). The x + 3 terms cancel out because they equal 1 and serve no purpose other than cluttering the expression. This leaves (x - 3)/(x - 5) as the simplified solution.
- Take all real zeros
Real zeros refer to any value that cause the expression to equal zero. Because zero terms nullify anything else, a single zero suffices. In this case, 3 works; however, 5 does not. This causes the denominator to equal zero, and division by zero is not mathematically acceptable.