1. PolynomialsPolynomials Today’s Objectives: Identify, Add & Subtract Polynomials Today’s Objectives: Identify, Add & Subtract Polynomials

2. already What you should already know / Monomials Monomials / Constants, Coefficients, & Degrees ConstantsCoefficientsDegrees / Properties of Powers Properties of Powers / Writing Differences as Sums Writing Differences as Sums / The Distributive Property The Distributive Property / Monomials Monomials / Constants, Coefficients, & Degrees ConstantsCoefficientsDegrees / Properties of Powers Properties of Powers / Writing Differences as Sums Writing Differences as Sums / The Distributive Property The Distributive Property

3. Monomial?# of terms?Polynomial?Binomial? Trinomial?

4. Polynomials / A polynomial is a monomial or sum of monomials / The monomials in a polynomial are called the terms of the polynomial. / x 2 +2x+1 has 3 terms: x 2,2x, & 1 / Binomials: Have 2 unlike terms / Trinomials: Have 3 unlike terms / A polynomial is a monomial or sum of monomials / The monomials in a polynomial are called the terms of the polynomial. / x 2 +2x+1 has 3 terms: x 2,2x, & 1 / Binomials: Have 2 unlike terms / Trinomials: Have 3 unlike terms

5. Determine whether each expression is a polynomial. If it is a polynomial, how many terms are there and state the degree of the polynomial. If it is not state why. Polynomial? How many Terms? Degrees? Polynomial? How many Terms? Degrees? Polynomial? How many Terms? Degrees? Polynomial? How many Terms? Degrees?

6. Using Algebra Tiles

7. Using Algebra Tiles: Simplify:

9. Example: Simplify:

11. Using Algebra Tiles: Simplify:

12. Example: Simplify

14. YOUR TURN!

15. / A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.

16. Monomials / A monomial is an expression that is a number, a variable, or the product of a number and one or more variables. / A monomial cannot contain variables in denominators, variables with exponents that are negative, or variables under radicals. / Constants Constants / Coefficients Coefficients / Degrees Degrees / A monomial is an expression that is a number, a variable, or the product of a number and one or more variables. / A monomial cannot contain variables in denominators, variables with exponents that are negative, or variables under radicals. / Constants Constants / Coefficients Coefficients / Degrees Degrees

17. Essential CharacteristicsNonessential Characteristics ExampleNon-Example Monomials

18. Constants / Monomials that contain no variables, / Example: 23 or -1 / Monomials that contain no variables, / Example: 23 or -1

19. Coefficient / The numerical factor of a monomial / Example: -6m -6 is the coefficient / The numerical factor of a monomial / Example: -6m -6 is the coefficient

20. Degree / Sum of the variables’ exponents. Where there are multiple terms; the highest sum of the exponents among each term. / Examples: 12g 7 h 4 7+4=11 3ax 6 +12y 7 z 2 6+1=7, 7+2=9 the degree is 9 / Sum of the variables’ exponents. Where there are multiple terms; the highest sum of the exponents among each term. / Examples: 12g 7 h 4 7+4=11 3ax 6 +12y 7 z 2 6+1=7, 7+2=9 the degree is 9

21. Properties of Powers / Power of a Power: (a m ) n =a mn / Power of a Product: (ab) m =a m b m / Power of a Quotient: (a/b) n = (a n /b n ); b  0 and (a/b) -n = (b/a) n = (b n /a n ); a  0, b  0 / Power of a Power: (a m ) n =a mn / Power of a Product: (ab) m =a m b m / Power of a Quotient: (a/b) n = (a n /b n ); b  0 and (a/b) -n = (b/a) n = (b n /a n ); a  0, b  0

22. Writing Differences as Sums / 2-7 = 2+(-7) / -6-11 = -6+(-11) / x-y = x+(-y) / 2-7 = 2+(-7) / -6-11 = -6+(-11) / x-y = x+(-y) / 8-2x = 8+(-2x) / 2xy-6yz = 2xy+(-6yz) / 6a 2 b-12 b 2c = 6a 2 b+(-12b 2 c)

23. The Distributive Property / -2(4x 3 +x-30)= -8x 3 -2x+6 / -1(x+2)= -x-2 / (-1/2)(3a+2)= (-3/2)a-1 / -2(4x 3 +x-30)= -8x 3 -2x+6 / -1(x+2)= -x-2 / (-1/2)(3a+2)= (-3/2)a-1

24. Algebra Tiles x2x2 x -x 1