Polynomial Functions and Adding and Subtracting Polynomials

1
5.2

• Polynomial Functions and Adding and Subtracting
  Polynomials

2
Polynomial Vocabulary

• Term a number or a product of a number and
  variables raised to powers
• Coefficient numerical factor of a term
• Constant term which is only a number
• Polynomial is a sum of terms involving variables
  raised to a whole number exponent, with no
  variables appearing in any denominator.

3
Polynomial Vocabulary

• In the polynomial 7x5 x2y2 4xy 7,
• there are ____terms
• The coefficient of term 7x5 is ____,
• of term x2y2 is ____,
• of term 4xy is ____ and
• of term 7 is ____.
• _____ is a constant term.

4
Types of Polynomials

• Monomial is a polynomial with one term.
• Binomial is a polynomial with two terms.
• Trinomial is a polynomial with three terms.

5
Degrees

• Degree of a term
• To find the degree, take the _______ of the
  exponents on the variables contained in the term.
• Degree of a constant is _____.
• Degree of the term 5a4b3c is ____ (remember that
  c can be written as c1).
• Degree of a polynomial
• To find the degree, take the largest degree of
  any term of the polynomial.
• Degree of 9x3 4x2 7 is 3.

6
Example

• If P(x) 3x2 2x 5, find the following,
• a. P(1)
• b. P(2)

7
Combining Like Terms

• ______________are terms that contain exactly the
  same variables raised to exactly the same powers.

Warning!
Only like terms can be combined through addition
and subtraction.
Example

• Combine like terms to simplify.
• x2y xy y 10x2y 2y xy

8
Adding Polynomials

• Adding Polynomials
• To add polynomials, combine all the like terms.

Example
Add. (3x 8) (4x2 3x 3)
9
Subtracting Polynomials

• Subtracting Polynomials
• To subtract two polynomials, change the signs of
  the terms of the polynomial being subtracted and
  then add.

Example
4 ( y 4)
a) Subtract
b) Simplify ( a2 1) (a2 3) (5a2 6a
7)