Factoring Quadratic Trinomials
🎯 Big Idea
Every quadratic trinomial with real roots can be broken down (factored) into simpler linear expressions. This is one of the most powerful techniques in algebra — it lets us rewrite complex expressions as products of simpler ones.
📐 Key Definitions
Quadratic Trinomial
A quadratic trinomial is an expression of the form:
$ax^2 + bx + c$
where $a \neq 0$, and $a$, $b$, $c$ are real numbers.
Root of a Quadratic Trinomial
A root of the quadratic trinomial $ax^2 + bx + c$ is a value of $x$ that makes the trinomial equal to zero. In other words, $x_0$ is a root if:
$ax_0^2 + bx_0 + c = 0$
We find roots by solving the quadratic equation $ax^2 + bx + c = 0$ using the quadratic formula: