Exponents3 5 82 2 2

34 122 2

73

4

22

2

33

12

2

02 14 4

4

3 3

5 5

4 4 42 2x x

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

Ex. (3ab2)4

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

Ex. x2nx2n

Ex.

Ex.

3 9

6 3

24

16

a b

a b

2

13

a

b

Ex. (2x-3y3)2

Ex.

21 2 3

2 5

2

4

x y

x y

A monomial is a number, variable, or a product of these

x

3x2

4x2y

The degree of a monomial is the sum of the powers of the variables

Polynomials

5x3

5 is the coefficient

x is the base

3 is the exponent or power

A polynomial is an expression made up of the sum of monomials, called terms

3x2 monomial

4x2y3 + 5 binomial

x4 – 5x + 6 trinomial

The degree of a polynomial is the greatest of the degrees of the terms

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

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

1 2 23 2 3P x x x

14 55 2 5V x x x

1 2 7P x x x

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)

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)

Ex. (3a3 – b + 2a – 5) + (a + b + 5)

Ex. (12z5 – 12 z3 + z) – (-3z4 + z3 + 12z)

Multiplying PolynomialsEx. -5y2(3y – 4y2)

Ex. 3a + 2a(3 – a)

Ex. 2a2b(4a2 – 3ab + 2b2)

When multiplying bigger polynomials, be sure each term is paired up

Ex. (x + 2)(x2 – 3x – 6)

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

Ex. (6x – 5)(3x – 4)

Ex. (2x2 – 3)(x2 – 2)

Ex. (3x – 2y)(2x + y)

Sum and Difference of Two Terms:

(a + b)(a – b) =

Ex. (2x – 1)(2x + 1)

Square of a Binomial:

(a + b)2 =

Ex. (5x – 3y)2