## How to Add and Subtract Polynomials

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The phrase "polynomial," as the name implies, is made up of the terms "**poly**" and "**nomial**," which relate to a variety of expressions. A polynomial is an algebraic or mathematical phrase consisting of **at least **two terms linked by a mathematical operation. Furthermore, the polynomial terms may include constants, variables, or a mixed term with a **co-efficient**. Furthermore, the variable's power (let's say \(x\)) in a polynomial should be an integer, **not **a **fractional **power like the squared or cube root.

For example, \(2x^{\frac{1}{3}} \ + \ 3x \ + \ 1\) is **not **a polynomial as the first term has a fraction power of \(x\).

### Types of Polynomials

Polynomials are classified into **three categories **based on the number of terms. Monomials, binomials, and trinomials are the three types. Let us go over these in greater detail:

**Monomial**: They consist of just a single term but there is one condition. The term cannot be zero. Ex: 6x², 7x³, 67x, etc.**Binomial**: Binomials consist of just two terms and they must have a mathematical operation in between. Ex: 6x² + 7x³, 8x² + 7y, xy² + 3x, etc.**Trinomial**: Trinomial consist of three terms and between every two terms there is a mathematical operation. Ex: 2x² + 3x + 10, 4x³ + 3x² + 7, 3x²y + 4xy + 6, etc.

### Degree of a Polynomial Expression

To know the degree of a **single variable **expression, follow these steps:

- First,
**simplify**the polynomial expression. - Then, write the polynomial expression in the
**standard form**. - Next, you should check and select the
**highest**exponent of the variable term.

**Ex**: \(4x^3 \ + \ 3x^2 \ + \ 7\) has the degree \(3\) since the **highest **exponent of \(x\) is \(3\).

To know the degree of a **multivariable **polynomial expression, follow these steps:

- First,
**simplify**the polynomial expression. - Then, write the polynomial expression in the
**standard**form. - Next, you should check and select the
**highest**exponent of the variable term. Note: you should add the powers of different variables too.

**Ex**: \(x^3 \ + \ 3x^2y^3 \ + \ 4\) has the degree \(5\), since the **middle **term has the power of \(x \ = \ 2\) and \(y \ = \ 3\), so the **addition **comes to \(5\).

### Addition and Subtraction in Polynomials

To do addition or subtraction in a polynomial expression, apply the below-mentioned steps:

- First, simplify the expression by adding/subtracting the like terms. Also. Don’t forget to apply
**PEMDAS**rule in case of brackets or parenthesis. - Also, wherever possible, use the distributive property.

**Ex**: \((3x^3 \ - \ 2) \ – \ (2x^3 \ + \ 4) \ = \ 3x^3 \ - \ 2x^3 \ - \ 2 \ – \ 4 \ = \ x^3 \ - \ 6\).

## Free printable Worksheets

### Exercises for Adding and Subtracting Polynomials

**1) **\((-9x \ + \ 8) \ + \ (6x \ - \ 6) = \)

**2) **\((6x \ + \ 3) \ + \ (2x \ - \ 2) = \)

**3) **\((-7x \ + \ 9) \ - \ (6x \ + \ 7) = \)

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

**5) **\((8x \ + \ 9) \ - \ (6x \ + \ 7) = \)

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

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

**8) **\((-3x^2 \ + \ 5x) \ + \ (5x^2 \ - \ 3x) = \)

**9) **\((-4x^2 \ + \ 7x) \ - \ (4x^2 \ + \ 5x) = \)

**10) **\((10x^2 \ + \ 5x) \ - \ (5x^2 \ + \ 4x) = \)

## Adding and Subtracting 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