Trinomials: Lead Coefficients Greater Than One

Instructor: Melanie Olczak

Melanie has taught high school Mathematics courses for the past ten years and has a master's degree in Mathematics Education.

This lesson defines polynomials and lead coefficients. Examples are given of how to write a polynomial in standard form and how to determine the lead coefficient.


Many people who think math is difficult often joke that they understood it until someone added letters. Unfortunately for those people, Algebra is mostly all variables.

A variable is a letter that represents an unknown number. So even though it may seem confusing to put letters in math, we are actually just using a letter to represent a number.

An expression that uses many variables is called a polynomial. The following are examples of polynomials:


The expressions below are not examples of polynomials:


The major difference between the examples and non-examples are the exponents of the variables. In all of the examples, the exponents are whole numbers, meaning, 0, 1, 2, 3, etc. In the non-examples, there are exponents which are negative, fractions, or the variable is in the denominator of the fraction.

A polynomial is the sum or difference of numbers, variables or the product of numbers and variables with whole number exponents.

Standard Form of a Polynomial

Whenever we write polynomials, we should write it in standard form. Standard Form of a Polynomial is when the terms are put in order from largest exponent to smallest exponent. The example below is a polynomial that is not in standard form.

non standard form

In order to put this in standard form, we need to take the term with the largest exponent. The largest exponent is 3, so we start with that term. The second largest exponent is 2, so that term comes second. The next term is the 'x' term; however, there are two, so we must first combine them.

polynomial standard form

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