Polynomial and rational functions

A polynomial's zeros can be found by factoring, and the Remainder Theorem helps: dividing by x-a leaves a remainder of p(a), so x-a is a factor (and a is a zero) exactly when that remainder is 0. For example, for p(x) = x^3 - 2x^2 - 5x + 6, p(1) = 1 - 2 - 5 + 6 = 0, so x-1 is a factor and 1 is a zero. Knowing a polynomial's zeros lets you sketch its rough graph, including its end behavior, and you can find where two functions intersect just by graphing them together and looking for where they cross. A rational expression like a(x)/b(x) can be rewritten as q(x) + r(x)/b(x) using division, and a rational or radical equation can be solved algebraically, though you should always check for extraneous solutions that don't actually satisfy the original equation.

This explanation is AI-generated and can occasionally be wrong. 🚩 Report