1. Exploring Polynomials & Radical Expressions
Chapter 5
Exploring Polynomials & Radical Expressions
By Wendi Kelson

2. 5-1 Monomials
A monomial is a number, variable, or a number and 1 or more variables multiplied together.
Examples: 10, x, 13y, ¼x3y4
A constant is a monomial that has just numbers & no variable.
The coefficient is the number in front of the variable.
Example: 5x → coefficient is 5
The degree of a monomial is the sum of the exponents.
Example: 18x6y3 → degree is 6+3 = 9

3. 5-1 Monomials (cont.) A power is an expression in the form xn.
Multiplying Powers → am * an = am+n
Example: 52 * 53 = 52+3 = 55
Dividing Powers → am/an = am-n
Example:
When c is a nonzero number, c0 = 1
y8 y*y*y*y*y*y*y*y
y y*y*y = =
y8-3 = y5

4. 5-1 Monomials (cont.) Properties of Powers
Power of a Power → (am)n = am*n
Example: (52)3 = 52*3 = 56
Power of a Product → (ab)m = am * bm
Example: (5*x)3 = 53 * x3 = 125x3
Power of a Quotient → (a/b)n = an/bn and (a/b)-n = (b/a)n
Examples: (5/3)2 = 52/32 = 25/9
(5/3)-2 = (3/5)2 = 32/52 = 9/25

5. 5-1 Practice What is the degree of 7x2y11? 2. Simplify x2 * x5.
3. Simplify y9/y5.
Answers: 1) ) x7 3) y4

6. 5-1 Practice (cont.) Simplify (z4)3. Simplify (2x)5. Simplify (2/5)-3.
Answers: 1) z12 2) 32x5 3) 125/8

7. 5-2 Polynomials
A polynomial is a monomial or the sum of 2 or more monomials.
Example: 2x2 + 3x + 1
The terms of a polynomial are the monomials that make it up.
Like terms in a polynomial are two terms that are the same except for their coefficients.
Example: In the equation 2x2 + 2x + x + 1, 2x and x are like terms and can be combined to 3x → 2x2 + 3x +1

8. 5-2 Polynomials
A polynomial with 2 unlike terms is called a binomial, and a polynomial with 3 unlike terms is called a trinomial.
The degree of a polynomial is the degree of the monomial with the biggest degree.
Example: The degree of 3x2 – 10x – 8 is 2.

9. 5-9 Complex Numbers Imaginary unit: i = √-1
A pure imaginary number is of the form bi, while the form a ± bi is a nonpure imaginary number.
A complex number is a number in the form of a ± bi, where a can be either zero or a real number.

10. 5-9 Complex Numbers
The Complex Number System