Transcript Slide 1

Chapter 5
Exploring Polynomials & Radical
Expressions
By Wendi Kelson
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
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: y8
y3
y*y*y*y*y*y*y*y
=
y*y*y
= y8-3 = y5
• When c is a nonzero number, c0 = 1
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
5-1 Practice
1. What is the degree of 7x2y11?
2. Simplify x2 * x5.
3. Simplify y9/y5.
Answers: 1) 13 2) x7 3) y4
5-1 Practice (cont.)
1. Simplify (z4)3.
2. Simplify (2x)5.
3. Simplify (2/5)-3.
Answers: 1) z12 2) 32x5 3) 125/8
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
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.
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.
5-9 Complex Numbers
The Complex Number System
(a + bi)
Complex
Numbers
(b ≠ 0)
Imaginary
Numbers
(b = 0)
Real
Numbers
Rational
Numbers
Irrational
Numbers
(a = 0)
Pure
Imaginary
Numbers
(a ≠ 0)
Nonpure
Imaginary
Numbers