A polynomial is an expression obtained by adding, subtracting, or multiplying one or more variables and constants and the powers of a variable. Each part of the sum is called a term.

The polynomial above has three terms. The degree of the polynomial is 2 (the highest power of the variables).

A one-term polynomial is called a monomial, a two-term polynomial is binomial and a three-term polynomial is a trinomial.

These are all polynomials. If there are more than 3 terms it is still called a polynomial. A polynomial consist of one or more monomials.

Example 1

The multiplicative factor of a variable is called the coefficient. If we have a monomial 2x, then the variable is x and the coefficient is 2.

Addition and subtraction of polynomials

When adding polynomials, all similar terms are added together. Similar terms are terms that have the same variable character and degree. Constant terms are also brought together.

Example 2

Below are two polynomials named P(x) and T(x).

The sum of the polynomials, P(x)+T(x)

We remove the parentheses and arrange similar terms side by side

We add similar terms together

Subtraction of polynomials P(x)-T(x)

We remove the parentheses and arrange similar terms side by side and add the terms together. Now the minus sign in front of the latter polynomial will change the signs for all terms after that.

Multiplication of polynomials

In multiplication of polynomials, all terms are multiplied with the multiplier.

Example 3

Below is the product where the binomial x - 2 is multiplied by the monomial 2x. We open the parenthesis by multiplying both terms of the binomial by 2x.

Example 4

Below is the product where binomial 2x + 2 is multiplied by binomial x-2. We open the parentheses by multiplying all terms with each other.

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