1. 5.2 Polynomials Objectives: Add and Subtract Polynomials
Multiply Polynomials

2. Vocabulary Binomial – a polynomial with 2 terms
Trinomial – a polynomial with 3 terms.
Degree of a polynomial – the highest degree of the monomials in the polynomial
For 5x⁶y²+2x⁴y³, the degree for each monomial is 8 and 7. The degree of the polynomial is 8 since it is higher.
Polynomial – a monomial or a sum of monomials such as
5x⁴-3y.
Terms – the monomials that make up a polynomial
Like terms – monomials with the same variable(s) with the same exponent on those variables.

3. Determine whether each expression is a polynomial
Determine whether each expression is a polynomial. If it is a polynomial, state the degree.
-4x⁵y²-6y³z⁸
yes, degree: 11 2.
not a polynomial
7x⁴-9x+3
yes, degree: 4

4. Adding and Subtracting Polynomials
Examples:
(2x²-5x+3)+(-4x²+x-9)=
-2x²-4x-6
(4a²-8a+2)-(7a²+6a-8)=
(4a²-8a+2)+(-7a²-6a+8)=
-3a²-14a+10
To add polynomials, add like-terms.
When adding or subtracting like-terms, add or subtract the coefficients, but not the exponents.
For subtraction, change signs of 2nd polynomial to opposites then use addition.

5. Multiplying a polynomial by a monomial
Use the distributive property. (multiply coefficients and add exponents on like-bases)
Example:
-3x²y³(5xy⁴-7x²y⁵)=
-15x³y⁷+21x⁴y⁸
⅔ab(-6a-9b+12ab)=
-4a²b-6ab²+8a²b²

6. Multiplying a Binomial by a Binomial
Use FOIL Method or Distributive Property
Examples: (FOIL)
(x-8)(4x+5)
4x²+5x-32x-40
4x²-27x-40
(a³-6)(a³+3)
a⁶+3a³-6a³-18
a⁶-3a³-18
Distributive Property:
(x-8)(4x+5)=
x(4x+5)-8(4x+5)=
4x²+5x-32x-40=
4x²-27x-40

7. Column Method and Box Method
(3x+6)(7x-5)
3x+6
x 7x-5
-15x-30
21x²+42x+ 0
21x²+27x-30
Box Method (helpful for multiplying trinomials)
(x-5)(2x+9) x 2x 9
2x²-x-45
2x²
-10x 9x
-45

8. Power of a Binomial
To take a binomial to a power, write that binomial down that number of times and use your method of choice for multiplying binomials.
Example: (2x-5)²
(2x-5)(2x-5)
4x²-10x-10x+25
4x²-20x+25

9. Homework Page even