Chapter 9.1 Notes: Add and Subtract Polynomials

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Chapter 9.1 Notes Add and Subtract Polynomials

• Goal You will add and subtract polynomials.

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• A monomial is a number, a variable with a
  positive integer exponent, or the product of a
  number and one or more variables with positive
  integer exponents.
• Monomials Not a Monomial
• 10
  5 x
• 3x
  2 / n
• ½ ab2
  4a
• -1.8m5
  x-1

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• The degree of a monomial is the sum of the
  exponents of the variables in the monomial.
• The degree of a nonzero constant term is 0.

Monomial Degree
10
3x
½ ab2
-1.8m5
7x2y5
-2x0
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• A polynomial is a monomial or a sum of monomials,
  each called a term of the polynomial.
• The degree of a polynomial is the greatest degree
  of its terms.
• When a polynomial is written so that the
  exponents of a variable decrease from left to
  right, the coefficient of the first term is
  called the leading coefficient.
• 2x3 x2 5x 12

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• Ex.1 Write 15x x3 3 so that the exponents
  decrease from left to right. Identify the degree
  and leading coefficient of the polynomial.
• Ex.2 Write 3b3 4b4 b2 so that the exponents
  decrease from left to right. Identify the degree
  and leading coefficient of the polynomial.

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• Binomials and Trinomials
• A polynomial with two terms is called a binomial.
• i.e. i.e.
  i.e.
• A polynomial with three terms is called a
  trinomial.
• i.e. i.e.
  i.e.

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• Ex.3 Tell whether the expression is a
  polynomial. If it is a polynomial, find its
  degree and classify it by the number of its
  terms. Otherwise, tell why it is not a
  polynomial.

Expression Is it a polynomial? Classify by degree and number of terms
9
2x2 x 5
6n4 8n
n-2 3
7bc3 4b4c
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• Ex.4 Find the sum or difference.
• a. -3b2 7b2
• b. 2xy 5xy
• c. 6x2z 13x2z
• d. -25b2 18b2
• Adding Polynomials
• (3x2 x 6) (x2 4x 10)
• Method 1
  Method 2

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• Ex.5 Find the sum.
• a. (-2x2 3x x3) (3x2 x3 12)
• b. (5x3 4x2 2x) (4x2 3x3 6)
• c. (5m2 m 2) (-3m2 10m 7)
• d. (7k2 2k 6) (3k2 11k 8)
• Subtracting Polynomials
• (8x2 7x 12) (2x2 4x 3)
• Method 1
  Method 2

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• Ex.6 Find the difference.
• a. (4x2 3x 5) (3x2 x 8)
• b. (2c2 8) (3c2 4c 1)
• c. (4x2 7x) (5x2 4x 9)
• d. (8x2 4x 12) (-2x2 7x 5)
• Ex.7 Find the sum or difference.
• a. (7m2 8m 3) (-3m2 4m 11)
• b. (-6x2 7x 9) (12x2 8x 5)
• c. (4x2 5x 6) (7x2 4x 3)
• d. (12x2 7x 10) (-12x2 9x 6)