In this lesson we will classify, add and subtract polynomials.

We can write 3a2b like this.. A monomial is a number, a variable or a product of numbers and variable(s). 3a2b is a monomial We can write 3a2b like this.. 3 · a · a · b

A polynomial is a monomial or the sum of two or more monomials 3a2b + 6a is a polynomial Each monomial in a polynomial is called a TERM

A polynomial can be classified by the number of terms A polynomial with 1 term is a monomial 5xy3 A polynomial with 2 terms is a binomial 3x + y3 A polynomial with 3 terms is a trinomial 2x2 + 3x –1

We can also classify polynomials by the highest exponent in the polynomial which is the degree of the polynomial The degree of 3x2 is 2 The degree of 5x + 3 is 1 The degree of 4x3 – 2x2 + 9 is 3

Classify the polynomial by the number of terms 7m3 + 2m This polynomial contains two monomials. This is a binomial

Classify this polynomial by degree 3x2 – 8x + 12 The first term in the polynomial has an exponent of 2 which is the highest exponent in the polynomial The polynomial is degree 2

We can model polynomials with algebra tiles 2x2 – 3x + 4

Add the two polynomials (x2 – 2x + 2) + (2x2 + 3x – 5) First model the polynomials Now add like terms

The result is 3x2 + x – 3 (x2 – 2x + 2) + (2x2 + 3x – 5)

Start by modeling each polynomial with tiles To subtract polynomials first use the distributive property which changes the sign for each term in the polynomial that is subtracted (2x2 + 2x – 1) – (x2 – x – 3) Start by modeling each polynomial with tiles

Here is the model for each polynomial (2x2 + 2x – 1) – (x2 – x – 3) Use the distributive property 2x2 + 2x – 1 – x2 + x + 3

Finally, add like terms 2x2 + 2x – 1 – x2 + x + 3 x2 + 3x + 2

Complete Activity 9a Classify Polynomials by the number of terms Classify Polynomials by degree Model Polynomials Add and Subtract Polynomials