3: Factoring
( \newcommand{\kernel}{\mathrm{null}\,}\)
- 3.1: Greatest Common Factor and Factor by Grouping
- This page discusses methods for finding the greatest common factor (GCF) and factoring polynomials. It includes examples, step-by-step instructions, and practice problems reinforcing these concepts, such as factoring expressions with negative leading coefficients and determining when polynomials cannot be factored. Additionally, it covers the reverse Distributive Property and features online resources for further learning.
- 3.2: Factor Quadratic Trinomials with Leading Coefficient 1
- This page offers a comprehensive tutorial on factoring trinomials, specifically in the forms x2+bx+c and x2+bxy+cy2. It guides readers through identifying factors based on the relationship between terms and provides examples and practice problems for reinforcement. Key points include recognizing the signs of factors affecting the middle term, handling cases with negative constants, and identifying prime trinomials that cannot be factored further.
- 3.3: Factor Quadratic Trinomials with Leading Coefficient Other than 1
- This page outlines strategies for factoring polynomials, particularly trinomials, emphasizing methods like the GCF, trial and error, and the "ac" method. It includes quizzes, examples, and practice problems to reinforce techniques such as checking combinations for factors and ensuring proper arrangement of terms. Key points include recognizing polynomial types, factoring completely, and considering sign conventions.
- 3.4: Factor Special Products
- The strategy for factoring we developed in the last section will guide you as you factor most binomials, trinomials, and polynomials with more than three terms. We have seen that some binomials and trinomials result from special products—squaring binomials and multiplying conjugates. If you learn to recognize these kinds of polynomials, you can use the special products patterns to factor them much more quickly.
- 3.5: General Strategy for Factoring Polynomials
- This page explains the complete factorization of polynomials through various methods, including identifying the greatest common factor (GCF), analyzing binomials and trinomials, and applying grouping techniques. It provides examples, outlines steps for recognizing patterns like perfect squares and sums or differences of squares and cubes, and emphasizes the need for verification of the factored form.