1. Polynomials 9-3-15

2. Polynomials  Examples : Monomials: 4f 3x 3 4g 2 2 Binomials: 4t + 9 9 – 7g 5x 2 + 7x 6x 3 – 8x Trinomials: x 2 + 2x + 3 5x 2 – 6x – 1 y 4 + 15y 2 + 100 Polynomials: x 3 – 3x 2 + 3x – 9 p 4 + 2p 3 + p 2 + 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 1 st NUMBER in front of the variable (line leader)

4. Special Kinds of Polynomials Degree (Largest Exponent) Name by Degree 0Constant 1Linear 2Quadratic

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

6. Special Names 4x 2 + 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 2 + 14 and 5x 2 + 2x 3x 2 + 0x + 14 + 5x 2 + 2x + 0 ____________ 8x 2 + 2x + 14

8. Adding Polynomials You try: 1.3y 2 + 8y + 2 and 2y 2 + 5 2.(y 2 + 3y – 7) + (2y 2 - y + 8) 3.-2p + 3 and 9p 2 – p + 4 4.12c 2 – 10c + 6 and -3c 2 + 2c – 6 5.(-4x 2 + 5x – 7) + (8x 2 – 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: (4y 2 + 8y + 9) – (2y 2 + 6y - 4) Change every sign in the second set of parentheses (4y 2 + 8y +9) + (-2y 2 – 6y + 4) Now add. 4y 2 + 8y + 9 + -2y 2 – 6y + 4 ____________ 2y 2 + 2y + 13

10. Subtracting Polynomials You try: 1.(3y 2 + 8y + 2) – (2y 2 + 5) 2.(y 2 + 3y – 7) - (2y 2 - y + 8) 3.(-2p + 3) - (9p 2 – p + 4) 4.(12c 2 – 10c + 6) – ( -3c 2 + 2c – 6) 5.(-4x 2 + 5x – 7) - (8x 2 – 7)

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