Welcome to the world of algebra! In this section, we will dive into the fascinating realm of factoring. Factoring is breaking down an equation or expression into simpler parts or factors that multiply together. Let's unlock the potential of polynomials and quadratic equations one factor at a time!
Basic Concepts
- Factor: A number or expression that divides another number or expression evenly.
- Greatest Common Factor (GCF): The largest factor that two or more numbers have in common.
- Prime Factorization: Breaking down a number into its prime number factors.
Factoring Techniques
- Common Factor Extraction: Identify and extract the greatest common factor from terms.
- Difference of Squares: Recognize patterns such as a2 - b2 and factor them accordingly.
- Trinomials: Deal with expressions of the form ax2 + bx + c with various methods including trial and error.
Example of Factoring Trinomials
Consider x2 + 5x + 6. We need two numbers that multiply to 6 and add up to 5. These numbers are 2 and 3. Thus, the factorization is:
x2 + 5x + 6 = (x + 2)(x + 3)
Interactive Exercises
Test your skills with our interactive exercises. Solve practice problems and receive instant feedback!