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section 3.3 dividing polynomials; remainder and factor theorems

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Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

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  • Slide 1
  • Section 3.3 Dividing Polynomials; Remainder and Factor Theorems
  • Slide 2
  • Long Division of Polynomials and The Division Algorithm
  • Slide 3
  • Slide 4
  • Long Division of Polynomials
  • Slide 5
  • Slide 6
  • Long Division of Polynomials with Missing Terms You need to leave a hole when you have missing terms. This technique will help you line up like terms. See the dividend above.
  • Slide 7
  • Slide 8
  • Example Divide using Long Division.
  • Slide 9
  • Example Divide using Long Division.
  • Slide 10
  • Dividing Polynomials Using Synthetic Division
  • Slide 11
  • Slide 12
  • Comparison of Long Division and Synthetic Division of X 3 +4x 2 -5x+5 divided by x-3
  • Slide 13
  • Steps of Synthetic Division dividing 5x 3 +6x+8 by x+2 Put in a 0 for the missing term.
  • Slide 14
  • Using synthetic division instead of long division. Notice that the divisor has to be a binomial of degree 1 with no coefficients. Thus:
  • Slide 15
  • Example Divide using synthetic division.
  • Slide 16
  • The Remainder Theorem
  • Slide 17
  • If you are given the function f(x)=x 3 - 4x 2 +5x+3 and you want to find f(2), then the remainder of this function when divided by x-2 will give you f(2) f(2)=5
  • Slide 18
  • Slide 19
  • Example Use synthetic division and the remainder theorem to find the indicated function value.
  • Slide 20
  • The Factor Theorem
  • Slide 21
  • Solve the equation 2x 3 -3x 2 -11x+6=0 given that 3 is a zero of f(x)=2x 3 -3x 2 -11x+6. The factor theorem tells us that x-3 is a factor of f(x). So we will use both synthetic division and long division to show this and to find another factor. Another factor
  • Slide 22
  • Example Solve the equation 5x 2 + 9x 2=0 given that -2 is a zero of f(x)= 5x 2 + 9x - 2
  • Slide 23
  • Example Solve the equation x 3 - 5x 2 + 9x - 45 = 0 given that 5 is a zero of f(x)= x 3 - 5x 2 + 9x 45. Consider all complex number solutions.
  • Slide 24
  • (a) (b) (c) (d)
  • Slide 25
  • (a) (b) (c) (d)

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