Don’t Hold Back Your Monomial Binomial Trinomial and try solving examples to get better idea. An algebraic expression that consists of just one term is called a monomial, with two terms is called binomial and with three terms is called trinomial.

Expression that consists of two or more terms is called a polynomial.

Monomials, binomials and trinomials are all types of polynomials. A polynomial is a formula that involves an x and a variable.

## Monomial:

Monomials are single terms that are present in algebraic expressions.

A monomial, binomial and trinomial are all mathematical terms used to describe different types of equations. . For example, a monomial would be written as x+4, a binomial would be written as x+4+2, and a trinomial would be written as x+4+2+7. All three terms can be used to represent various equations, such as linear equations, quadratic equations and polynomials.

It can be a constant, a variable, or a constant times one or more variables. For example, 5, x are all monomials. Monomials can be positive or negative and can have whole number or fractional exponents.

## Binomial:

Binomial is same as monomial but with two terms.

Binomials can be positive or negative. Examples of binomial are 14x+3, x^2+5, 17x^2-6

## Trinomial:

Trinomial is same as monomial but with three terms.

Trinomials can be positive or negative. Examples of binomial are 10x^2+14x+3, x^2-15x+5, 17x^2+26x-6

## Degree of a Polynomial:

The degree of a polynomial is the highest degree assigned to any individual term. For example, given the polynomial (or trinomial):

10x^2 + 14x – 6, let’s evaluate the degree of each term—or, in other words, the highest exponent when a term consists of only a single variable.

**Note:**

The degree of any constant is always zero (0). Thus, -1.3, 3.14, 5, 58, etc. all have a degree of 0 since there is no variable associated with the value.

The first term has the highest exponent (which is 2), so the degree of 10x^2 +14x – 6 is 2.

Let’s consider another example and find the degree of this polynomial: a + a^3b^2 – c^4. When two or more variables are present in a term, the degree is the sum of that term’s exponents.

The greatest degree of the terms is 5 (because the sum of the exponents of the term a^3b^2 is 5). So the degree of a + a^3b^2 – c^4 is 5. Terms are usually listed in order by degree so that the terms should be typed as a^3b^2 – c^4 + a

## Standard Form:

The standard form of a polynomial is when the expression is simplified (with all like terms combined) and the terms are arranged so the degree of each term decreases or stays the same from left to right. These two different polynomials are shown in standard form:

r^4 – 4r^3 + 7r^2 – 2r + 5

x^5 – 8x^3 + 7x^2 – x

Notice that the expressions have been arranged so that the terms with the largest degree (that is, the largest exponents) are first, followed by the terms with successively smaller degrees.

## Evaluating Polynomials:

The following equation involves a polynomial which represents the braking distance B (in feet) that is needed to stop a car; where v is the car’s speed per hour and r is the reaction time of the driver

B = 1.47vr + 0.05v^2

If a car was going 80 miles an hour and the driver took two seconds to react, how long would it take the car to stop? Substituting these values for v and r, we have

1.47(80)(2) + 0.05(80)^2 = 235.2 + 320 = 555.2

Thus, it would take the car approximately 555.2 feet to stop.

## How to Determine the Rule for Finding the Sum of Monomials, Binomials and Trinomials?

To find the sum of monomials, simply add the coefficients of the terms with the same variables and exponents.

Each term within the expression must be added or subtracted to another term.

- An algebraic expression that consists of just one term is called a
**monomial** - An expression that consists of two or more terms is called a polynomial
- The degree of any constant is always zero (0)
- Monomial, Binomial and Trinomial can be a constant, a variable, or a constant times one or more variables. It can be positive or negative and can have a whole number or fractional exponents.

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