Factoring Polynomials Overview

This page provides a comprehensive guide on factoring different types of polynomials, including difference of squares, trinomials, and polynomials with 4 terms. Each factoring method is explained with step-by-step instructions and examples.

Difference of Squares

The first section covers factoring difference of squares polynomials. These are polynomials in the form a²-b².

Definition: The difference of squares formula is a+b$$a-b = a²-b².

To factor, identify the terms that are perfect squares and apply the formula.

Example: x²-64 factors to x+8$$x-8

Example: 18m²n-2n³ factors to 2n3m+n$$3m-n

Trinomials

The guide then explains how to factor trinomials, both with and without leading coefficients.

For trinomials in the form x²+bx+c:

1. Find factors of c that add up to b
2. Write the factored form x+p$$x+q

Example: x²-x-42 factors to x-7$$x+6

For trinomials with leading coefficients (ax²+bx+c), the "Slip and Slide" method is introduced.

Example: 30x²-27x+6 factors to 3$10x²-9x+2$, which further factors to 32x-1$$5x-2

Grouping Method

The final section covers factoring polynomials using grouping method, which is useful for polynomials with 4 terms.

Example: $2a³-a²b$+$10a-5b$ factors to a²+5$$2a-b

Highlight: Always look for a Greatest Common Factor (GCF) before applying other factoring methods.

This guide provides a comprehensive overview of factoring polynomials, equipping students with the tools to tackle various types of polynomial factoring problems.