1. Polynomials Review
Just in case you forgot….

2. In a nutshell... Simplifying polynomials (gathering like terms)
Naming polynomials (# of terms and degree)
Adding
Subtracting
Multiplying
Dividing

3. Simplifying Polynomials
Terms are alike if:
They have the same degree
They have the same variable
Add the coefficients of like terms (watch out for positive and negative signs!)
2x3+x2-3x3-4+2x-1
-x3+x2+2x-5

4. Naming Polynomials By # of terms: 1 term: monomial 2 terms: binomial
3 terms: trinomial
4+ terms: polynomial
By degree:
Zero degree: constant
1st degree: linear
2nd degree: quadratic
3rd degree: cubic
4th degree: quartic
5th degree: quintic
6th+ degree: nth degree

5. Adding and subtracting
The same as combining like terms, easy!
Remember to watch your positive and negatives!
Also remember to only combine terms with the same variable and degree.
Subtracting:
Switch all the signs of any polynomial that comes after a minus sign. Then add like normal!
(2x2+x+2) - (3x2-2x+4)
(2x2+x+2)+(-3x2+2x-4)
2x2+x+2-3x2+2x-4
-x2+3x-2

6. Multiplying and Dividing
Use the power law and distributive property
-x(2x3-x2+8)
Dividing
Use the quotient law and distributive property
(5x2-35x+15)/(5)
-1x1(2x3-1x2+8x0)
(5x2-35x1+15x0)/(5x0)
-2x4+x3-8x
x2-7x+3

7. Using Algebra tiles Adding and Subtracting
Lay tiles out like a normal expression
Flip over tiles if you are subtracting them, then add.
Multiplying and Dividing
Multiplication and division table

8. Multiplying with algebra tiles
2x(-x+2) X 1 1 X X

9. Multiplying with algebra tiles
2x(-x+2) X 1 1 X X

10. Multiplying with algebra tiles
2x(-x+2) = -2x2+4x X 1 1 X X2 X X X X2 X X

11. Dividing with algebra tiles
(2x2-4x)/-2x = X X2 X X X X2 X X

12. Dividing with algebra tiles
(2x2-4x)/-2x = X X2 X X X X2 X X

13. Dividing with algebra tiles
(2x2-4x)/-2x = -x+2 X 1 1 X X2 X X X X2 X X

14. Types of questions you might see on the test
Naming polynomials
Simplifying polynomials
Adding/subtracting polynomials
Multiplying/Dividing polynomials
All of the above with algebra tiles
Perimeter Questions
Area questions
“Create a polynomial” questions
“Cost modelling” questions
Maybe a binomial x binomial???

15. Polynomials PAT Questions (2013)