Factoring

Definition

Factoring is the process of breaking down an expression into a product of simpler expressions, often polynomials. It simplifies solving equations by expressing them as a product of factors.

5 Must Know Facts For Your Next Test

1. The most common method for factoring quadratic equations is to express them in the form $ax^2 + bx + c$.
2. A quadratic equation can be factored if its discriminant $b^2 - 4ac$ is a perfect square.
3. Factoring can reveal the roots (solutions) of a quadratic equation by setting each factor equal to zero.
4. The Zero Product Property states that if $ab = 0$, then either $a = 0$ or $b = 0$.
5. Common factoring techniques include grouping, using the difference of squares formula, and completing the square.

Review Questions

• What form does a quadratic equation need to be in to apply factoring?
• How does the Zero Product Property help in solving factored equations?
• What condition must be met for a quadratic equation to be easily factorable?

Related terms

Quadratic Equation:

An equation of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.

Discriminant:

$b^2 - 4ac$; determines the nature and number of roots of a quadratic equation.

Zero Product Property:

If a product of factors equals zero, at least one of the factors must equal zero.