Factorization

Factorization is the process of breaking down numbers or algebraic expressions into their constituent parts that, when multiplied together, yield the original number or expression.

Integer Factorization

• Prime Factorization: For integers, finding the prime numbers that multiply to give the number. For instance, $12=2\times 2\times 3$.

Algebraic Factorization

• Common Factor Method: Identifying the greatest common factor (GCF) of the terms in an expression and factoring it out, like in $6x+9=3(2x+3)$.
• Difference of Squares: Factoring expressions like $x^2-4$ into $(x+2)(x-2)$.
• Quadratic Equations: Breaking down expressions like $6x^2+5x+6$ into two binomials, as in $(x+2)(x+3)$.
• Grouping Method: Creating a common factor by grouping terms, e.g., $2x^3+2x^2-3x-3=(x+1)(2x^2-3)$.
• Trial and Error / Factor Pairs: Systematically testing pairs to find factors, e.g., factors of $24$ are $1\times 24$, $2\times 12$, $3\times 8$, and $4\times 6$.
• Completing the Square: Creating perfect square trinomials, like in $x^2+6x+9=(x+3{)}^2$.
• Prime Factorization: Breaking numbers down into a product of their prime factors, such as $60=2^2\times 3\times 5$.