Trinomial

A trinomial is a polynomial with exactly three terms. The most common form is the quadratic trinomial $ax^2 + bx + c$, which is the right-hand side of every standard quadratic equation.

Special trinomial patterns to recognise:

• Perfect square trinomial: $a^2 + 2ab + b^2 = (a + b)^2$. Spot when first and last terms are perfect squares and the middle is twice their product.
• Quadratic factorable over integers: $x^2 + bx + c$ factors as $(x + p)(x + q)$ when integers $p, q$ exist with $p + q = b$ and $pq = c$.
• AC method for $ax^2 + bx + c$ ($a \neq 1$): find numbers multiplying to $ac$, adding to $b$.

Trinomials are practice ground for factoring techniques that scale to higher polynomials: GCF, grouping, AC method.