MTH 091

1
MTH 091

• Section 10.3
• Introduction to Polynomials
• Section 10.4
• Adding and Subtracting Polynomials

2
What Is A Polynomial?

• A polynomial is an algebraic expression with
  counting number exponents on .
• Parts of a polynomial
• Variables
• Constants
• Coefficients
• Terms are separated by addition and subtraction
  signs.
• Polynomials can be classified by type.
• One term monomial
• Two terms binomial
• Three terms trinomial
• More than three terms polynomial

3
More About Polynomials

• Polynomials can also be classified by degree.
• The degree is the largest exponent on any term.
• If the terms have more than one variable, add
  the exponents on each term to get the degree of
  that term.
• A polynomial written in descending order has the
  terms arranged from greatest exponent to least
  exponent.

4
For the polynomial -6x64x57x3-9x2-1, complete
the chart below

• Term Coefficient Degree
• 7x3
• -9
• 6
• 4
• -1

5
Evaluating A Polynomial

• Evaluating a polynomial is the same as evaluating
  an algebraic expression (substitute and
  simplify).
• Recall that the order of operations requires that
  we perform exponents before we perform
  multiplication.

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Examples

• Find the degree and type of each polynomial
• -6y 4
• a 5a2 3a3 4a4
• 7r2 2r 3r5
• Evaluate each polynomial for x -1
• x2 3x 4
• -2x3 3x2 6

7
Adding Polynomials Like Terms Revisited

• Recall that like terms will have the same
  variables, with the same exponents on those
  variables.
• When we add or subtract like terms, we add or
  subtract the coefficients only. DO NOT add the
  exponents!

8
Subtracting Polynomials

• Apply Keep-Change-Change
• Keep the first polynomial.
• Change the subtraction sign between polynomials
  to an addition sign.
• Change the signs of all the terms in the second
  polynomial.
• Add.

9
Add or Subtract as Indicated