Description

This topic is completely devoted to the reverse operation from multiplying, factoring. In this topic, we explore many more advanced problems than Elementary Algebra in factoring polynomials. Sections covered within this topic include factoring monomial factors and factoring by grouping; factoring trinomials with leading coefficient 1 or not 1; factoring special types of polynomials such as the difference of two squares, perfect square trinomials and the sum and difference of two cubes as well as more factoring by grouping; general methods of factoring; solving nonlinear equations by factoring and solving applied problems by factoring.

Sections of this topic include:

1. Monimial Factors; Factoring by Grouping

   Beginning this section, we investigate factoring out monomial factors as well as factoring by grouping. Groups within this section include: factoring monomial factors; factoring out common factors; factoring out common binomial factors; factoring out common monomial factors with variable power; and factoring by grouping.

2. Factoring Type I Trinomials

   We next focus on factoring trinomials with a leading coefficient of 1 (called Type I Trinomials). Groups within this section include: Factoring trinomials; factoring trinomials with common factors; factoring trinomials with substitutions; factoring trinomials with common binomial factors; factoring trinomials with common factors of variable powers; factoring trinomials with common factors that are decimals.

3. Factoring Type II Trinomials; a Test for Factorability

   We next exploring factoring trinomaisl that do not have a leading coefficient of 1 (called Type II Trinomials). We also explore factoring random polynomials. Groups within this section include: factoring trinomials with leading coefficent other than 1; factoring random polynomials.

4. Factoring Special Types of Polynomials; More Factoring by Grouping

   In saving time factoring, we investigate patterns of polynomials that match factoring formulas. Groups in this section include: factoring the difference of two squares; factoring sums or differences of two cubes; and factoring perfect square trinomails.

5. General Methods of Factoring.

   With so many ways and types of factoring, we explore a general strategy of factoring any given polynomial.

6. Solving Nonlinear Equations by Factoring

   With the ability to factor, we turn our attention in solving nonlinear equations by factoring and using the zero product rule.

7. More Applications; Solving Applied Problems by Factoring

   This section addresses of solving applied problems by solving equations using factoring and the zero product rule.