1. Polynomials
9-3-15

2. Examples: Polynomials
Monomials: 4f
3x3
4g2 2
Binomials:
4t + 9
9 – 7g
5x2 + 7x
6x3 – 8x
Trinomials:
x2 + 2x + 3
5x2 – 6x – 1
y4 + 15y
Polynomials:
x3 – 3x2 + 3x – 9
p4 + 2p3 + p2 + 9p - 5
Polynomials are algebraic expressions. This group of expressions include monomials, binomials, trinomials.
Monomials: contain ONE term
Binomials: contain TWO terms
Trinomials: contain THREE
*Any expression with more than three terms is just called a polynomial.
**REMEMBER: TERMS are separated by the operation symbols.

3. Specifics of a Polynomial
Degree: the exponent of the variable
Degree of the Polynomial: Highest (largest) exponent of the polynomial
Standard Form: Terms are placed in descending order by the DEGREE
Leading Coefficient: Once in standard form, it’s the 1st NUMBER in front of the variable (line leader)
k + 4
2x2 – 9x +7
6y3 – 5y2 - y

4. Special Kinds of Polynomials
Degree (Largest Exponent)
Name by Degree
Constant 1
Linear 2
Quadratic

5. Special Names -2y -9 Degree: 1
Degree Name: Linear # of Terms Name: Binomial
Leading Coefficient: -2

6. Degree Name: Quadratic # of Terms Name: Trinomial
Special Names x2 + 3x -7
Degree: 2
Degree Name: Quadratic # of Terms Name: Trinomial
Leading Coefficient: 4

7. Adding Polynomials
When adding polynomials, make sure the exponents are variables are the same on the terms you are combining.
The easiest way to do this is to line them up in columns.
Example: Add 3x and 5x2 + 2x
3x2 + 0x + 14
+ 5x2 + 2x + 0
____________
8x2 + 2x + 14

8. Adding Polynomials
Examples: Add (4x3 – 2x) + (-x3 - 4) 4x3 – 2x x3 + 0x – 4 _______________ 3x3 + 2x – 4
You try:
3y2 + 8y + 2 and 2y2 + 5
(y2 + 3y – 7) + (2y2 - y + 8)
-2p + 3 and 9p2 – p + 4
12c2 – 10c + 6 and -3c2 + 2c – 6
(-4x2 + 5x – 7) + (8x2 – 7)

9. Subtracting Polynomials
When you subtract polynomials, it is important to remember to change ALL the signs in the subtracted polynomial (the one listed second) and then add. Example: (4y2 + 8y + 9) – (2y2 + 6y - 4) Change every sign in the second set of parentheses (4y2 + 8y +9) + (-2y2 – 6y + 4) Now add. 4y2 + 8y y2 – 6y + 4 ____________ 2y2 + 2y + 13

10. Subtracting Polynomials
Example: Add (4x3 – 2x) - (-x3 - 4) Change every sign in the second set of parentheses (4x3 – 2x) + ( x3 + 4) Now add. 4x3 – 2x x3 + 0x + 4 _______________ 5x3 - 2x + 4
You try:
(3y2 + 8y + 2) – (2y2 + 5)
(y2 + 3y – 7) - (2y2 - y + 8)
(-2p + 3) - (9p2 – p + 4)
(12c2 – 10c + 6) – ( -3c2 + 2c – 6)
(-4x2 + 5x – 7) - (8x2 – 7)

11. Ticket out the Door Add. Subtract. (11t3 – 4t2 + 3) + (-t3 + 4t2 – 5)
(3p2 + 2p – 1) – (-5p2 – p +8)