1. Algebra I Section 9.1 – 9.2 Review
Polynomials
Algebra I
Section 9.1 – 9.2 Review

2. Polynomials Polynomial: A monomial or a sum of monomials.
Monomial: 1 term 4xy2
Binomial: 2 terms 5x - 1
Trinomial: 3 terms 3x2 – 2x + 1
Polynomial: 4 terms or more

3. Degree of a Polynomial
To find the degree of a polynomial (if it is a: monomial), add the exponents on the variables contained in each term.
Note: If more than one term has the same degree, arrange the terms by which single base has the highest degree.
Examples:
1. 8y a xy2z

4. Degree of a Polynomial
Constant = 0
Linear = 1
Quadratic = 2
Cubic = 3

5. Classifying Polynomials
–3x5 + 9x3 + 7
Trinomial
Degree 5
5x4y6
Monomial
Degree 10
–8xy + 15x
Binomial
Degree 1
6x6 + 2x3 + 3x2
Trinomial
Degree 6

6. Standard Form of a Polynomial
Place the terms of the polynomial in order from the least degree to greatest degree.
Example: Put the trinomial below in standard form.
9x3 + 7 – 3x5

7. Polynomial Standard Form Practice
3x2 – 6x2y2 + 4x3
-x4 + 2xy + 7xy4
-9rx + r5x
15km – 13m3 + 10k3

8. Adding & Subtracting Polynomials
(3x2 – 4x + 8) + (2x – 7x2 – 5)
Combine “like-terms” and put solution in standard form.

9. Practice Adding & Subtracting Polynomials
(4x + 5xy + 3y) – (3y + 6x + 8xy)

10. Methods for Multiplying Polynomials by Polynomials
Distribute
FOIL
Box

11. Multiplying Polynomials Using Distribution
Multiplying Monomials by Polynomials: Use the distributive property.
Remember the Rule of Multiplying Numbers with Exponents (add the exponents)
Examples:
-2x2(3x2 – 7x + 10)

12. Practice Multiplying Polynomials Using Distribution
4(3d2 + 5d)
5x3(x2 – 2x + 6)
6x(2x2 – 4x) – (x + 2)

13. FOIL Method
FOIL: only works when multiplying a binomial times a binomial.
First – 1st terms in each parenthesis
Outer – 1st term in 1st parenthesis times last term in 2nd parenthesis
Inner – Last term in 1st parenthesis times 1st term in 2nd parenthesis
Last – Last term in 1st parenthesis times the last term in 2nd parenthesis

14. Using FOIL (3x + 5)(x + 6) First Outer Inner Last
__________ + _________ + _________ + __________
F O I L

15. Practice Using FOIL (x + 5)(x + 6) (5m + 2)(7m + 3) (8b – 3)(-2b +6)
(9p + 6)(6p – 2)

16. Box Method
Box Method works with all types of polynomials. The size of the box depends on how many terms are in the polynomials.
Example: binomial x trinomial = 2 x 3 box

17. How to use the Box Put each factor on the outside of a box.
Multiply to fill the box
Combine like-terms (add) to empty the boxes
Be sure to simplify your answer.

18. How to Use the Box Method
(x + 2)(3x2 + 2x + 1)

19. Practice Using the Box Method
(k + 4)(7k2 + 2k – 9)
(2x2 – 9x + 11)(2x + 1)

20. Polynomial Word Problems
The length of a pool is (2x2 + 3x) and the width is (x – 2). Find the area of the pool.

21. Polynomial Word Problems
Kenny wants to build a sidewalk around a rectangular garden that is 3 feet wide. If the width of the garden is 2x and the length is 3x + 1, find the area of the sidewalk.
3x x 3’