Factoring

Definition

Factoring involves breaking down an expression into a product of simpler expressions, often to solve equations or simplify. It is particularly useful for solving quadratic equations.

5 Must Know Facts For Your Next Test

1. The standard form of a quadratic equation is $ax^2 + bx + c = 0$.
2. The most common method for factoring quadratics is finding two numbers that multiply to $ac$ and add to $b$.
3. Quadratic equations can often be factored using techniques like grouping, the difference of squares, and perfect square trinomials.
4. If a quadratic equation cannot be factored easily, the quadratic formula or completing the square may be used instead.
5. Factoring is essential for solving higher-degree polynomials by reducing them into simpler quadratic forms.

Review Questions

• What are the steps to factor the quadratic equation $x^2 - 5x + 6 = 0$?
• How do you determine if a quadratic equation can be factored?
• What methods can you use if direct factoring of a quadratic equation is difficult?

Related terms

Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$; provides solutions to any quadratic equation.

Completing the Square: A method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve.

Difference of Squares: $a^2 - b^2 = (a+b)(a-b)$; a technique used in factoring where both terms are perfect squares.