1. Do Now: Aim: How do we work with polynomials?
Evaluate each expression for x = -2.
1) -x + 1
2) x2 - 5
3) -(x – 6)
Simplify each expression.
4) (x + 5) + (2x + 3)
5) (x + 9) – (4x + 6)
6) (-x2 – 2) – (x2 – 2)

2. Warm Up

3. Warm Up - Answers

4. Degree of a Monomial 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.

5. Polynomials in One Variable
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.

6. Polynomials in One Variable
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 1st degree polynomial. 1st degree polynomials are linear.
This is a 2nd degree polynomial. 2nd degree polynomials are quadratic.
This is a 3rd degree polynomial. 3rd degree polynomials are cubic.

7. Standard Form
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.

8. Remember: The lead coefficient should be positive in standard form.
Examples
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.

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

10. The degree of a Monomial
Is the sum of the exponents of the variables of the monomial.
Monomial Degree x
x3 y2 5
3x3 y
32x3 y2 5

11. The degree of a Polynomial
Is the highest degree of any of its terms after the poly has been simplified.
Polynomial Degree 2
3x2 + 5x + 7

12. Descending order of Polynomials
From the highest degree to the lowest degree of the terms.
3x2 + 5x + 7
3x3 + 5x2 - 2x + 7 2 1 2 1 3

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

14. Simplify
Combine like terms and put terms in descending order

15. Simplify

16. Simplify
*Notice that (a+b) 2 = a2 +2ab +b2

17. Simplify

18. Note: Simplify: (x + y) (x2 – xy + y2)
= x3 – x2y + xy2 + x2y – xy2 + y3
Simplify: (x – y) (x2 + xy + y2)
= x3 + x2y + xy2 – x2y – xy2 + y3
Note:

19. Simplify