Factoring

Factoring is a mathematical process used in number theory, algebra, and calculus. It involves breaking down a composite number or a polynomial into a product of smaller, simpler factors.

Factoring Numbers

When factoring numbers, the goal is to write the number as a product of prime numbers. For example, the factors of 12 are 2, 2, and 3, since 12 = 2 * 2 * 3.

Factoring Polynomials

When factoring polynomials, the goal is to write the polynomial as a product of lower-degree polynomials.

For example, the polynomial x^2 + 5x + 6 can be factored into (x + 2)(x + 3).

Common techniques for factoring polynomials include:

• Factoring out the Greatest Common Factor (GCF): If each term in the polynomial shares a common factor, that factor can be factored out.
• Factoring by Grouping: This method is used when a polynomial has four or more terms. The terms are grouped and a common factor is factored out of each group.
• Factoring Quadratics: Quadratic polynomials (degree 2) can often be factored into the product of two linear terms.
• Factoring by Special Formulas: Certain forms of polynomials, such as the difference of squares or perfect square trinomials, can be factored using special formulas.

Applications

Factoring is a fundamental skill in algebra that is used to simplify expressions, solve polynomial equations, and evaluate integrals in calculus. Understanding factoring is essential for further study in mathematics and many related fields, such as physics and engineering.