Adding and Subtracting Polynomials

1
Adding and Subtracting Polynomials

• Module VII, Lesson 1
• Algebra Online
• VHS_at_PWCS

2
What is a polynomial?

• A polynomial is one term or the sum or difference
  of two or more terms.
• Examples of polynomials are
• We classify polynomials by degrees or by number
  of terms.

3
Classifying by Degree

• Degree of a term is the exponent of the term.
• x4 2x2 4
• The degree of a polynomial is the degree for the
  term with the highest power. In this case it is
  4.

The degree of this term is 4.
The degree of 2x2 is 2
The degree of any constant is 0.
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Classifying by Degrees

• Polynomials with degrees of 0 3 have special
  names. They are
• 0 degree constant
• 1st degree linear
• 2nd degree quadratic
• 3rd degree - cubic

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Classifying By Number of Terms

• Polynomials can also be named by the number of
  terms that make it up.
• One term (6xy)
• Monomial
• Two terms (4x 9)
• Binomial
• Three terms (5d2 5d 10)
• Trinomial
• Three or more terms is considered a polynomial

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Classify each polynomial by its degree and
number of terms.

1. Quadratic monomial
2. Cubic trinomial
3. 4th degree binomial
4. 0 degree constant

1. 2x2
2. 4b3 3b 8
3. -2t4 5t
4. 5

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Simplifying Polynomials

• Recall from earlier lessons that to add or
  subtract terms they must have exactly the same
  variable.
• 5x2 12x2
• 2w3 4w 3w3
• -3r3 5r3 8r3
• 14x 9

17x2
Just add or subtract the coefficients of terms
with the same variable
5w3 4w
-6r3
14x - 9
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Adding Polynomials

• (5x2 3x 7) (2x2 5x - 7)
• To add these polynomials we just add the like
  terms. The easiest way to do this is like we
  always have added. Line them up on top of each
  other and add.

7x2 2x
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Subtracting Polynomials

• (2x3 4x2 6) (3x3 2x 2)
• Recall that subtracting is the same as adding the
  opposite. So change everything in the second
  polynomial to its opposite and add.

-x3 4x2 2x - 4
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Try some on your own.

1. (3y2 5y 6) (7y2 9)
2. (9y 7x 15a) (-3y 8x 8a)
3. (7a 10b) (3a 4b)
4. (5x2 4) (3x2 8x 4)

1. 10y2 5y 15
2. 6y x 7a
3. 4a 14b
4. 2x2 8x - 8

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Wrap-Up

• Polynomials can be classified by degree
  (constant, linear, quadratic or cubic) or number
  of terms (monomial, binomial and trinomial).
• Terms can only be added or subtracted if they
  have the exact same variable.