Remainder Factor Theorems May 27 2009

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Remainder Factor Theorems May 27 2009

  1. 1. What are the factors of 15?
  2. 2. 2 Is x ­ 3 a factor of  2x  ­ 4x ­ 3   Long division: 
  3. 3. 2 Is x ­ 3 a factor of  2x  ­ 4x ­ 3   Synthetic Division: 
  4. 4. Remainder Theorem:  If P(x) is a polynomial, then P(a) is equal  to the remainder when P(x) is divided by  x ­ a. 
  5. 5. 4 2 Is x + 3 a factor of  x  ­ 10x  ­ 2x + 4
  6. 6. Factor Theorem:  A polynomial P(x) has a factor x ­ a  if and only if P(a) = 0
  7. 7. Determine whether x + 2 is a factor of 3 f(x) = x  ­ 6x ­ 4
  8. 8. 3 2 Is x + 2 a factor of  x  + 4x  + 5x + 2
  9. 9. 3 2 Divide  6x  + 16x  ­ 19x  ­ 4 by  x ­ 2
  10. 10. 4 2 Divide x  ­ 10x  ­ 2x + 4 by  x + 3
  11. 11. 4 2 Divide x  ­ 10x  ­ 2x + 4 by  x + 3
  12. 12. Completely factor 3 2 f(x) = x  ­ 2x  ­ 5x + 6 constant term
  13. 13. Completely factor:  3 2 f(x) = 2x  + 3x  ­ 8x + 3 (x ­ 1)(x + 3)(2x ­ 1)
  14. 14. Exercise 53 Questions 1 ­ 8

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