Algebra II: Factoring
Introduction and Summary
Algebra I dealt with some factoring--we leaned how to factor equations of the form a 2 + bx + c , as well as perfect square trinomials and the difference of squares. This chapter explains how to factor other polynomials.
Section one explains how to factor trinomials of degree 2 with a leading coefficient--that is, trinomials of the form ax 2 + bx + c , where a , b , and c are integers. This section outlines the steps for factoring these trinomials. The process for factoring ax 2 + bx + c is a generalization of the process for factoring x 2 + bx + c , which we learned in Algebra I.
The second section explains how to factor some polynomials of degree 3. First, it deals with polynomials which are the difference of cubes, then with polynomials which are the sum of cubes. Finally, the second section explains how to factor equations of the form ax 3 + bx 2 + cx + d where = .
The next section focuses on fourth degree polynomials. It explains how to factor a difference of fourth powers, as well as some fourth-degree trinomials.
Finally, in the fourth section, we learn one of the most important uses of factoring--finding roots. The roots of a function are the solutions to f (x) = 0 ; i.e. the points at which y = f (x) crosses the x -axis. Learning how to find roots will help when graphing polynomial equations. Learning how to find the number of roots will also allow us to approximate the shape of a graph without plugging in points.
Finding the roots of an equation becomes especially important in the study of polynomials in Algebra II and higher mathematics. Thus, it is crucial to understand how to factor an equation. Factoring takes practice; it is more useful to try several problems and get a feel for factoring than it is to memorize a set of steps for factoring. This chapter does provide a set of steps--they are meant to be used as a framework or skeleton until the reader becomes more familiar with factoring. The reader is encouraged to practice factoring, as it will come up a lot in Algebra II.