Do Now: Evaluate each expression for x = -2. Aim: How do we work with polynomials? 1) -x + 12) x ) -(x – 6) Simplify each expression. 4) (x + 5) + (2x + 3) 5) (x + 9) – (4x + 6) 6) (-x 2 – 2) – (x 2 – 2)

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What is the degree of the monomial? The degree of a monomial is the sum of the exponents of the variables in the monomial. The exponents of each variable are 4 and = 6. The degree of the monomial is 6. The monomial can be referred to as a sixth degree monomial.

A polynomial is a monomial or the sum of monomials Each monomial in a polynomial is a term of the polynomial. The number factor of a term is called the coefficient. The coefficient of the first term in a polynomial is the lead coefficient. A polynomial with two terms is called a binomial. A polynomial with three terms is called a trinomial.

The degree of a polynomial in one variable is the largest exponent of that variable. A constant has no variable. It is a 0 degree polynomial. This is a 1 st degree polynomial. 1 st degree polynomials are linear. This is a 2 nd degree polynomial. 2 nd degree polynomials are quadratic. This is a 3 rd degree polynomial. 3 rd degree polynomials are cubic.

The degree of a Monomial Is the sum of the exponents of the variables of the monomial. x 3 3 x 3 y 2 5 MonomialDegree 3x 3 y x 3 y 2 5

Find the degree for each polynomial: Degree: 3 Degree: 5

3. Find the perimeter of the triangle. P = (6a - 5) + (3a + 2) + 3a P = 12a - 3

Combine like terms and put terms in descending order Simplify

*Notice that (a+b) 2 = a 2 +2ab +b 2

Simplify

Simplify: (x + y) (x 2 – xy + y 2 ) Simplify: (x – y) (x 2 + xy + y 2 ) = x 3 – x 2 y + xy 2 + x 2 y – xy 2 + y 3 = x 3 + x 2 y + xy 2 – x 2 y – xy 2 - y 3 Note:

Simplify