# What is a trinomial expression?

A trinomial is an expression made up of 3 terms (“3 bits of algebra”). However, make sure that the exponents of any variables are positive whole numbers (no negative exponents are allowed). However, the coefficients of each term can be anything (negative, fractions, surds etc..)

Here are some examples of trinomials:

2x² + 4x + 1

5y⁴ + 2y² - 8y

3x²y³ - 6x⁴ + 1/2x

3n – 4p + 6qr

8y⁴ -1/3x³ + 8x²

Example 1

Decide if this expression is a trinomial or not. Explain your answer.

3x⁴ + 2x²

This expression is not a trinomial as there are only 2 terms. In fact, this is binomial expression.

Example 2

Decide if this expression is a trinomial or not. Explain your answer.

x² + x + 3

This expression is a trinomial as there are exactly 3 terms in the expression and all the powers are positive integers. In fact, the expression is a quadratic trinomial as the highest power of x is 2.

Example 3

Decide if this expression is a trinomial or not. Explain your answer.

x⁴ + 2x⁻³ + x²

This expression is not a trinomial as the 2^{nd} term in the expression has a negative exponent.

Example 4

Decide if this expression is a trinomial or not. Explain your answer.

3x⁴y² - 4x²+7z⁴

Just like example 2 this is a trinomial, as the expression contains 3 terms and the exponents are all positive whole number.

Example 5

Decide if this expression is a trinomial or not. Explain your answer.

4x⁻⁴ + 2x³ + 4x

This is not a trinomial as the first term of the expression contains a negative exponent.

Example 6

Decide if this expression is a trinomial or not. Explain your answer.

5x⁷ -x³ + 3/x

Just like example 5 this expression contains a negative exponent because 3/x can be rewritten as 3x⁻¹. Therefore the expression is not a trinomial.

## Comments

Your quest to make mathematical concepts straight forward is up there with the Holy Grail. I'm wobdering catman3000 if you would also include how, when & why some of these concepts / formulae are used. Thanks again.

How do you solve a trinomial when the "power" sign is a letter and not a number? Like this example that you gave: x? + 2x?³ + x². Can it be solved without a number?