1. Polynomials A polynomial is a sum of monomials. Common polynomials:
A binomial is a sum of two monomials.
A trinomial is a sum of three monomials.

2. (the powers go from greatest to least)
Standard Form
The terms of a polynomial are usually written so that the powers of the variable are in descending form.
(the powers go from greatest to least)
Ex. Write 7x2 – x4 in standard form.
2x4 + 7x2 – 11

3. Rewrite each polynomial so that the powers of x are in descending form.
6x2 + 5 – 8x – 2x3
2) 2xy3 + y2 + 5x3 – 3x2y

4. Adding & Subtracting Polynomials
To add or subtract polynomials,
1) Align The Like Terms
2) Add/Subtract The Like Terms
*Subtracting is the same as adding the opposite!!
** When adding or subtracting, EXPONENTS STAY THE SAME!!

5. 1. Add the following polynomials (9y – 7x + 15a) + (-3y + 8x – 8a)
Line up your like terms.
9y – 7x + 15a
+ -3y + 8x – 8a
_________________________ 6y
+ x
+ 7a

6. 2. Add the following polynomials (3a2 + 3ab – b2) + (4ab + 6b2)
_________________________
3a2
+ 7ab
+ 5b2

7. 3. Add the following polynomials (4x2 – 2xy + 3y2) + (-3x2 – xy + 2y2)
Line up your like terms.
4x2 – 2xy + 3y2
+ -3x2 – xy + 2y2
_________________________
x2 - 3xy + 5y2

8. 4. Subtract the following polynomials (9y – 7x + 15a) – (-3y +8x – 8a)
Line up your like terms and add the opposite.
9y – 7x + 15a
+ (+ 3y – 8x + 8a)
12y
– 15x
+ 23a

9. 5. Subtract the following polynomials (7a – 10b) – (3a + 4b) 4a
– 14b

10. 6. Subtract the following polynomials (4x2 – 2xy + 3y2) – (-3x2 – xy + 2y2)
7x2 – xy + y2

11. 7. Subtract (2x2 – 5a2 + 7x) from (5x2 + 3a2 – 5x).
From Comes First!!!!
7. Subtract (2x2 – 5a2 + 7x) from (5x2 + 3a2 – 5x).
(5x2 + 3a2 – 5x) – (2x2 – 5a2 + 7x)
The polynomial after FROM goes first!!!!
5x2 + 3a2 – 5x
+ (- 2x2 + 5a2 – 7x)
3x2 + 8a2 – 12x

12. 8. Subtract (5x2 – 4) from (3x2 + 8x + 4).
(3x2 + 8x + 4) – (5x2 – 4)
3x2 + 8x + 4
+ (- 5x )
-2x2 + 8x + 8

13. Find the sum or difference. (5a – 3b) + (2a + 6b)

14. Find the sum or difference. (5a – 3b) – (2a + 6b)