1. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Rules for Exponents
Product Rule
Power Rule 1
Power Rule 2
Power Rule 3

2. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Simplify the Following: 1. 2. 3. 4.

3. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Simplify the Following: 1.
x^9y^5 2.
r^27 3.
a^6b^12c^24 4.
(k^6m^15)/(n^9p^12)

4. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Polynomial: a finite sum of terms with only positive or zero integer coefficients permitted for the variables.
The Degree of the polynomial is the highest coefficient.
Monomial: 1 term
Binomial: 2 terms
Trinomial: 3 terms
Example: Here is a polynomial
The degree is 9, and it is a trinomial

5. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Adding and Subtracting Polynomials is done by combining like terms.
Example: Simplify each expression 1. 2. 3. 4.

6. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Adding and Subtracting Polynomials is done by combining like terms.
Example: Simplify each expression 1.
7y^3 + 5y – 4 2.
4a^5 + 6a^4 – 4a^3 + 9a^2 3.
3b^3 – b^4 + 9 4.
8x^5 – 16x^4 + 24x^2 – 4x^5 – 2x^4 + 16x^2 =
4x^5 – 18x^4 + 40x^2

7. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Multiplying Polynomials-multiply each term of the first polynomial by each term of the second polynomial, then combine like terms.
Example: Simplify each expression 1. 2. 3. 4.

8. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Multiplying Polynomials-multiply each term of the first polynomial by each term of the second polynomial, then combine like terms.
Example: Simplify each expression 1.
2y^2 + 2y - 12 2.
4x^2 – 25 3.
a^4 – 5a^3 + 11a^2 – 10a 4.
16w^6 + 48w^3 + 36

9. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Dividing Polynomials: the quotient can be found using an algorithm similar to the long division model used for whole numbers. Both polynomials must be written in descending order.
Example: What is the quotient of /65?
Use the process of long division.

10. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Dividing Polynomials: the quotient can be found using an algorithm similar to the long division model used for whole numbers. Both polynomials must be written in descending order.
Example: What is the quotient of /65?
Use the process of long division. 42
65)2730
260
130

11. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Dividing Polynomials
Example: Find the quotient

12. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Dividing Polynomials
Example: Find the quotient
Quotient: 5x^2 + 4x (no remainder)

13. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Dividing Polynomials
Example: Find the quotient

14. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Dividing Polynomials
Example: Find the quotient
Quotient: 5x^2 - 26
(remainder of 104x + 3)

15. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Dividing Polynomials
Example: Find the quotient

16. Section R3: Polynomials
223 Reference Chapter
Section R3: Polynomials
Dividing Polynomials
Example: Find the quotient
Quotient: 6a^3 – 30a^ a
(remainder of -748a)