## How to Classify Polynomials

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Polynomials appear in lots of forms. They may differ via the **number** of **terms,** or monomials, which make up the polynomial, plus they additionally might differ via the **degrees** of the monomials in the polynomial. At this time, we are going to look at **several methods** of classifying polynomials. Firstly, we’ll categorize polynomials via the number of terms in the polynomial. After that, we’ll categorize them via the monomial that has the **biggest exponent.**

### Find Polynomials, Monomials, Binomials, and Trinomials

Monomials, or sums and/or difference of monomials, is known as polynomials. Polynomials comprising \(2\) terms, like \(4x \ + \ 6\), are known as **binomials.** If the polynomial contains \(3\) terms, like in \(7x^2 \ + \ 2x \ + \ 3\), it is known as a **trinomial.****polynomial—Monomial,** or 2 or more monomials, **combined** by addition or subtraction (“poly” stands for **many**)**monomial—Polynomial** with precisely **one** term (“mono” stands for one)**binomial—Polynomial** with precisely \(2\) terms (“**bi**” stands for **two**)**trinomial—Polynomial** with precisely \(3\) terms (“**tri**” stands for **three**)

### Here are a few examples of polynomials:

Polynomial |
\(z \ + \ 4\) | \(2b^2 \ - \ 3b \ + \ 9\) | \(7q^6 \ - \ 2q^5 \ - \ 3q^3 \ + \ 9\) |

Monomial |
\(r^7\) | \(35\) | \(-11x^4\) |

Binomial |
\(q^2 \ - \ 5\) | \(-3p \ + \ p^4\) | \(6y \ + \ 3\) |

Trinomial |
\(6y \ + \ 3y^7 \ - \ 2y^9\) | \(8q^5 \ + \ 3q^2 \ - \ 5q\) | \(z^3 \ - \ 5z \ + \ 4z^4\) |

Note that **every** monomial, binomial, and trinomial is additionally a **polynomial.** They’re **special members** in the family of polynomials which have special names. The words ‘monomial’, ‘binomial’, and ‘trinomial’ are used whenever you want to refer to these special polynomials, then you may call all the rest of them ‘polynomials’.

### Figuring out the Degree of Polynomials

It is possible to calculate a polynomial’s degree via determining the **highest power** of the variable which occurs in it. You can **classify** polynomials using the polynomial’s degree. The polynomial’s **degree** is the degree of its **highest** degree term. Therefore, the degree of \(-2y \ + \ y^4 \ - \ y^6\) is \(6\).

Polynomials are said to be written in **standard form** whenever the terms are placed from the **highest to** the **lowest** degree. Whenever they are written using the standard form it’s simple to figure out the polynomial’s degree. The term having the highest degree is known as a **leading term** since it’s written **first** in the standard form. The leading term’s coefficient is known as a **leading coefficient**.

### Exercises for Classifying Polynomials

**1) **\(-8x + 7\)\( \ \Rightarrow \ \)

**2) ** \(9x^6 + 4x^5 - 6x^4\)\( \ \Rightarrow \ \)

**3) **\(6x + 2\)\( \ \Rightarrow \ \)

**4) **\(-1x + 2\)\( \ \Rightarrow \ \)

**5) **\(-6x^2 + 6x - 7\)\( \ \Rightarrow \ \)

**6) **\(8x^2 + 1x - 4\)\( \ \Rightarrow \ \)

**7) **\(-12x^2 + 5x - 4\)\( \ \Rightarrow \ \)

**8) **\(-8x^4 + 2x^3 - 1x^2 + x \)\( \ \Rightarrow \ \)

**9) **\(5x^2 - 6x^3 \)\( \ \Rightarrow \ \)

**10) **\(7x^4 + 7x^3 - 3x^2 + x \)\( \ \Rightarrow \ \)

## Classifying Polynomials Practice Quiz

### More Polynomials courses

- How to Classify Polynomials
- How to Write Polynomials in Standard Form
- How to Multiply Monomials
- How to Simplify Polynomials
- How to Add and Subtract Polynomials
- How to Multiply a Polynomial and a Monomial
- How to Multiply Binomials
- How to Do Operations with Polynomials
- How to Factor Trinomials
- How to Divide Monomials