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Section 4-3

Section 4-3. The Remainder and Factor Theorems. Remainder Theorem. Remainder Theorem – If a polynomial P(x) is divided by x-r, the remainder is a constant, P(r), and where Q(x) is a polynomial with degree one less than the degree of P(x ). Example 1. Synthetic Division by x+3.

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Section 4-3

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  1. Section 4-3 The Remainder and Factor Theorems

  2. Remainder Theorem Remainder Theorem – If a polynomial P(x) is divided by x-r, the remainder is a constant, P(r), and where Q(x) is a polynomial with degree one less than the degree of P(x).

  3. Example 1

  4. Synthetic Divisionby x+3 Remainder 13

  5. Divide using synthetic division. By y+2

  6. Divide using synthetic division. By y+2 -2 -1 0 4 0 3 2 0 2 -4 0 0 -6 8 -1 2 0 0 3 -4 8 Remainder of 8

  7. Divide using synthetic division. By (x+2)

  8. Divide using synthetic division. By (x-1)

  9. Divide using synthetic division. By (x+1)

  10. Divide using synthetic division. By (x-4)

  11. Example 3

  12. Example 4

  13. Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomialby (x+1)

  14. Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomialby (x+4)

  15. Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomialby (x-1)

  16. Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomialby (x-4)

  17. Example 5

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