1. Exponents 1 1 1 1

2. Ex. (-2a2b3)(-4ab2)
Ex. (3ab2)4
Ex. (-2a2b)3(-3ab2)2

3. Ex. x2nx2n
Ex.

4. Ex. (2x-3y3)2
Ex.

5. Polynomials A monomial is a number, variable, or a product of these x
4x2y
The degree of a monomial is the sum of the powers of the variables 5 5 5 5

6. 5x3
5 is the coefficient
x is the base
3 is the exponent or power

7. The degree of a polynomial is the greatest of the degrees of the terms
A polynomial is an expression made up of the sum of monomials, called terms
3x2  monomial
4x2y  binomial
x4 – 5x + 6  trinomial
The degree of a polynomial is the greatest of the degrees of the terms 7 7 7 7

8. P(x) = 7x4 – 3x2 + 2x – 4
This is a polynomial function
7, -3, 2, and -4 are called coefficients
Note that the terms are in descending order with respect to powers
7 is called the lead coefficient because it is the coefficient for the largest power of x
-4 is called the constant term because it is not multiplied by the variable

9. Coefficients can be any real number, but powers of a polynomial must be whole numbers (no negatives or fractions)

10. Ex. If P(x) = -5x3 + x2 + 3x – 2, find:
a) P(-1)
b) P(2)
c) The degree of P(x)
d) The lead coefficient of P(x)

11. When adding and subtracting polynomials, combine like terms (same variables to the same powers)
Ex. (4x2 + 3x – 5) + (x2 – 7x + 10)
Ex. (5x2 – x + 6) – (-2x2 + 3x – 11)

12. Ex. (3a3 – b + 2a – 5) + (a + b + 5)
Ex. (12z5 – 12 z3 + z) – (-3z4 + z3 + 12z)

13. Multiplying Polynomials
Ex. -5y2(3y – 4y2)
Ex. 3a + 2a(3 – a)
Ex. 2a2b(4a2 – 3ab + 2b2) 13 13 13 13

14. When multiplying bigger polynomials, be sure each term is paired up
Ex. (x + 2)(x2 – 3x – 6) 14 14 14 14

15. Multiplying a binomial by a binomial can be organized by remembering FOIL
(3x – 2)(2x + 5)
First
Outer
Inner
Last
6x2
15x
-4x
-10
6x2 + 11x – 10 15 15 15 15

16. Ex. (6x – 5)(3x – 4) Ex. (2x2 – 3)(x2 – 2) Ex. (3x – 2y)(2x + y) 16 16

17. Sum and Difference of Two Terms:
(a + b)(a – b) =
Ex. (2x – 1)(2x + 1)

18. Square of a Binomial:
(a + b)2 =
Ex. (5x – 3y)2