Exploring Polynomials

1
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 63 9

3
5-1 Monomials (cont.)

• A power is an expression in the form xn.
• Multiplying Powers ? am an amn
• Example 52 53 523 55
• Dividing Powers ? am/an am-n
• Example
• When c is a nonzero number, c0 1

y8 yyyyyyyy y3 yyy


y8-3 y5
4
5-1 Monomials (cont.)Properties of Powers

• Power of a Power ? (am)n amn
• Example (52)3 523 56
• Power of a Product ? (ab)m am bm
• Example (5x)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) 13 2) 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 v-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