What is a trinomial?
To understand the concept of trinomial, we should know what a monomial is. A monomial is an algebraic expression that has only one term.
For example: - 2a, 4x, 6z are all monomials. A trinomial is a polynomial which consists of three monomial terms. For example: -
• 2a+3b-4c
• 4x-84-6z
They both are the examples of trinomials.
Factoring trinomials
Rules to factor trinomials: (how to factor trinomials)
A trinomial expression is an algebraic expression which has exactly three terms. Trinomials can either be quadratic equation or a higher order equation. In case it is a quadratic equation, it can be simplified either by factoring or using quadratic formula.
For example: - 2x^2-7x+6 can be written as 2x^2-4x-3x+6 which can be factored as (2x-3) (x-2) so this is how we factor trinomials if they are in quadratic form.
A higher order trinomial can be turned into a quadratic equation by factoring common terms and then can be factored again.
For example: - 6x^2y + 14xy + 4y
In this expression, we have 2y common in all terms, so we can take that common, so that becomes
2y (3x^2+7x+2)
And that can further be factored as 2x (3x+1) (x+2).
Following instructions should be followed for solving trinomials: -
• First, factor the common factors from all the terms. For example if we have 3x^2+24x+45 then we can take 3 common from all the terms and write the expression like this, 3(x^2+8x+15).
• Check the trinomial equation you are left with.
• If the highest power of the trinomial equation is 2, then it can be factored like a quadratic equation
• If the highest power is the higher degree, then we should look for a pattern that allows you to solve it like a quadratic equation.
• Solve the quadratic part of the equation and make the factors.
