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.

To rewrite a polynomial in standard form, rearrange the terms of the polynomial starting with the largest degree term and ending with the lowest degree term. The leading coefficient, the coefficient of the first term in a polynomial written in standard form, should be positive.

Write the polynomials in standard form. Remember: The lead coefficient should be positive in standard form. To do this, multiply the polynomial by –1 using the distributive property.

The degree of a Monomial Is the sum of the exponents of the variables of the monomial. MonomialDegree x 1 x y 2 9 0

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

The degree of a Polynomial Is the highest degree of any of its terms after the poly has been simplified. Polynomial Degree 3x 2 + 5x + 7 2

Descending order of Polynomials From the highest degree to the lowest degree of the terms. 3x 2 + 5x + 7 3x 3 + 5x 2 - 2x + 7

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