1. ALGEBRA 1 UNIT 8 POLYNOMIAL EXPRESSIONS (See Part 2 for Factoring)
Unit Essential Questions
Are two algebraic expressions that appear to be different actually equivalent?
What is the relationship between properties of real numbers and properties of polynomials?

2. ADDING AND SUBTRACTING POLYNOMIALS
MACC.912.A-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
MACC.912.A-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.

3. WARM UP
Simplify. 1) 2) 3)
8x + 2y
h + 5j
–4a + 5b

4. KEY CONCEPTS AND VOCABULARY
A monomial is a real number, a variable, or the product of real numbers and variables (Note: the variables must have positive integer exponents to be a monomial). The degree of a monomial is the sum of the exponents of its variables. A polynomial is a monomial or a sum of monomials. Standard form of a polynomial means that the degrees of its monomial terms are written in descending order. The degree of a polynomial is the same as the degree of the monomial with the greatest exponent.

5. KEY CONCEPTS AND VOCABULARY
CLASSIFICATION OF POLYNOMIALS
DEGREE
NUMBER OF TERMS
Constant 1
Monomial
Linear 2
Binomial
Quadratic 3
Trinomial
Cubic 4
Polynomial with 4 terms
EXAMPLES OF
MONOMIALS
EXAMPLES OF NOT 6 g

6. EXAMPLE 1: IDENTIFYING POLYNOMIALS
Determine whether each expression is a polynomial. If it is a polynomial, classify the polynomial by the degree and number of terms. a) b) c) d)
Polynomial,
Cubic Trinomial
Not a Polynomial 5
Polynomial,
Quadratic
Binomial
Polynomial,
Constant
Monomial

7. EXAMPLE 2: WRITING POLYNOMIALS IN STANDARD FORM
Write the polynomial in standard form. Then identify the leading coefficient. a) b) c)
Leading Coefficient = 3
Leading Coefficient = –2
Leading Coefficient = 8

8. EXAMPLE 3: ADDING POLYNOMIALS
Simplify. a) b)

9. EXAMPLE 4: SUBTRACTING POLYNOMIALS
Simplify. a) b)

10. EXAMPLE 5: SIMPLIFYING USING GEOMETRIC FORMULAS
Express the perimeter as a polynomial. a) b)

11. EXAMPLE 6: ADDING AND SUBTRACTING POLYNOMIALS IN REAL-WORLD APPLICATIONS
The equations and represent the number of Miami Heat hats, H, and the number of Cleveland Cavalier hats, C, sold in m months at a sports store.
Write an equation for the total, T, of Heat and Cavalier hats sold.
Predict the number of Heat and Cavalier hats sold in 9 months.
267 Hats

12. RATE YOUR UNDERSTANDING
ADDING AND SUBTRACTING POLYNOMIALS
MACC.912.A-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
MACC.912.A-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.
RATING
LEARNING SCALE 4
I am able to
add and subtract polynomials in real-world applications or in more challenging problems that I have never previously attempted 3
identify a polynomial and write polynomials in standard form
add and subtract polynomials 2
identify a polynomial and write polynomials in standard form with help
add and subtract polynomials with help 1
identify the degree of a monomial
TARGET

13. MULTIPLYING A POLYNOMIAL BY A MONOMIAL
MACC.912.A-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

14. WARM UP
Simplify. 1) 2) 3)

15. KEY CONCEPTS AND VOCABULARY
You can use the Distribution Property to multiply a monomial by a polynomial.

16. EXAMPLE 1: MULTIPLYING A POLYNOMIAL BY A MONOMIAL
Simplify. a) b)

17. EXAMPLE 2: SIMPLIFYING EXPRESSIONS WITH A PRODUCT OF A POLYNOMIAL AND A MONOMIAL
Simplify. a) b)

18. EXAMPLE 3: SIMPLIFYING USING GEOMETRIC FORMULAS
Express the area as a polynomial. a) b)

19. EXAMPLE 4: SOLVING EQUATIONS WITH POLYNOMIALS ON EACH SIDE
Solve. a) b)
x = –1

20. RATE YOUR UNDERSTANDING
MULTIPLYING A POLYNOMIAL BY A MONOMIAL
MACC.912.A-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
RATING
LEARNING SCALE 4
I am able to
multiply a polynomial by a monomial in more challenging problems that I have never previously attempted (such as solving equations) 3
multiply a polynomial by a monomial 2
multiply a polynomial by a monomial with help 1
understand that the distributive property can be applied to polynomials
TARGET

21. MULTIPLYING POLYNOMIALS
MACC.912.A-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

22. WARM UP
Simplify. 1) 2) 3)

23. KEY CONCEPTS AND VOCABULARY
METHODS FOR MULTIPLYING POLYNOMIALS
DISTRIBUTIVE PROPERTY METHOD
FOIL METHOD
Example:

24. EXAMPLE 1: FINDING THE PRODUCT OF TWO BINOMIALS USING THE DISTRIBUTIVE PROPERTY
Simplify using the distributive property. a) b) c)

25. EXAMPLE 2: FINDING THE PRODUCT OF TWO BINOMIALS USING THE FOIL METHOD
Simplify using the FOIL method. a) b) c)

26. EXAMPLE 3: FINDING THE PRODUCT OF A BINOMIAL AND TRINOMIAL
Simplify using the distributive property. a) b) c)

27. EXAMPLE 4: SIMPLIFYING PRODUCTS
Simplify. a) b)

28. RATE YOUR UNDERSTANDING
MULTIPLYING POLYNOMIALS
MACC.912.A-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
RATING
LEARNING SCALE 4
I am able to
multiply two binomials or a binomial by a trinomial in more challenging problems that I have never previously attempted 3
multiply two binomials or a binomial by a trinomial 2
multiply two binomials or a binomial by a trinomial with help 1
understand the distributive property
TARGET

29. SPECIAL PRODUCTS
MACC.912.A-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

30. WARM UP
Simplify. 1) 2) 3)

31. KEY CONCEPTS AND VOCABULARY
MULTIPLYING SPECIAL CASES
THE SQUARE OF A BINOMIAL
THE PRODUCT OF A SUM AND DIFFERENCE
(a + b)2 = (a + b)(a + b) = a2 + 2ab + b2 Or
(a – b)2 = (a – b)(a – b) = a2 – 2ab + b2
(a + b)(a – b) = a2 – b2

32. EXAMPLE 1: SIMPLIFYING THE SQUARE OF A BINOMIAL (SUM)
Simplify. a) b) c)

33. EXAMPLE 2: SIMPLIFYING THE SQUARE OF A BINOMIAL (DIFFERENCE)
Simplify. a) b) c)

34. EXAMPLE 3: SIMPLIFYING THE PRODUCT OF A SUM AND DIFFERENCE
Simplify. a) b) c) d)

35. EXAMPLE 4: SIMPLIFYING MORE CHALLENGING PROBLEMS WITH SPECIAL CASES
Simplify. a) b) c) d)

36. EXAMPLE 4: SIMPLIFYING MORE CHALLENGING PROBLEMS WITH SPECIAL CASES
Simplify. e) f)

37. RATE YOUR UNDERSTANDING
SPECIAL PRODUCTS
MACC.912.A-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
RATING
LEARNING SCALE 4
I am able to
simplify special products in more challenging problems that I have never previously attempted 3
find the square of a binomial
find the product of a sum and difference 2
find the square of a binomial with help
find the product of a sum and difference with help 1
understand that there are special rules to simplify the square of a binomial and the product of a sum and difference
TARGET