Definition: A trinomial is a polynomial with exactly three unlike terms, for example x^2 + 5x + 6 or 2a^3 – 4a + 11.
What is a trinomial?
Three terms, none of which can be combined with another. The best-known family is the quadratic trinomial ax2 + bx + c.
Where do trinomials come from?
They appear when you multiply two binomials, and they are what you factor to undo that multiplication. They also arise when you square a binomial.
Example. Factor x2 + 11x + 24. Look for two numbers with product 24 and sum 11. The pairs of 24 are 1 and 24, 2 and 12, 3 and 8, 4 and 6. The pair 3 and 8 adds to 11. So x2 + 11x + 24 = (x + 3)(x + 8). Expanding (x + 3)(x + 8) returns x2 + 8x + 3x + 24, which confirms the answer.
What can go wrong?
When the constant term is negative, the two numbers have opposite signs, and the larger one takes the sign of the middle coefficient. Students also try to factor when the leading coefficient is not 1 using the same shortcut, which fails; those trinomials need grouping or trial and error.
Where to learn it
- Combining and Multiplying Polynomials – lesson
- Factoring Polynomials with Patterns and Grouping – lesson