Adding & Subtracting Polynomials I can and I will operate with polynomials and simplify results.

What is a polynomial? An expression which is the sum of terms of the form where k is a nonnegative integer. A Polynomial has no variables in the denominator. Also, the exponents cannot be variables.

Monomial - An expression that is a number, a variable, or a product of a number and one or more variables. It is a polynomial with only one term Examples: A Monomial can be thought of as a bicycle with 1 wheel; a unicycle.

Binomial: A polynomial of two terms. Examples: A binomial can be thought of as a bicycle.

Trinomial: A polynomial of three terms. Examples: A trinomial can be thought of as a tricycle.

The DEGREE of each term of a polynomial is the exponent of the variable. The DEGREE of a POLYNOMIAL is the largest degree of its terms.

POLYNOMIALS are usually written in STANDARD FORM, which means that the terms are placed in descending order, from largest degree to smallest degree. Example:

Classified by number of terms Classifying Polynomials Classified by number of terms Polynomial Degree 6 monomial –2 x 1 monomial 3x + 1 1 binomial –x 2 + 2 x – 5 2 trinomial 4x 3 – 8x 3 binomial 2 x 4 – 7x 3 – 5x + 1 4 polynomial

Add: VERTICAL FORMAT: Write each expression in standard form and line up like terms. Add the coefficients. HORIZONTAL FORMAT: Group like terms and add coefficients

Horizontal method Vertical method Ex. 1) (Rewrite and combine like terms) Vertical method

Ex. 2)

Watch This!

Ex. 3)

Ex. 4) :

You Try! 1) 2)

Reflection… Is 6 a polynomial? Explain. Describe the 3 types of polynomials and give an example of each.

Exit Ticket… Find the sum or difference.

Time to Practice! p. 557-558 #1-35 odd; 37-39 all