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Polynomial and Synthetic Division

Polynomial and Synthetic Division. By the Definition of Exponents. Notice that 5 – 3 = 2. Examples. Monomial division of a polynomial. Example 2. Long Division. Check. Long Division. Check. x 2 times. 1. x goes into x 3 ?. 2. Multiply (x-1) by x 2. 3. Change sign, Add.

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Polynomial and Synthetic Division

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  1. Polynomial and Synthetic Division

  2. By the Definition of Exponents Notice that 5 – 3 = 2

  3. Examples

  4. Monomial division of a polynomial

  5. Example 2

  6. Long Division. Check

  7. Long Division. Check

  8. x2 times. 1. x goes into x3? 2. Multiply (x-1) by x2. 3. Change sign, Add. 4. Bring down 4x. 5. x goes into 2x2? 2xtimes. 6. Multiply (x-1) by 2x. 7. Change sign, Add 8. Bring down -6. 9. x goes into 6x? 6times. 10. Multiply (x-1) by 6. 11. Change sign, Add .

  9. Divide.

  10. Example = Check

  11. Synthetic Division. 1 -8 +15 3 3 -15 0 1 -5

  12. Synthetic Division. 1 -2 -8 3 3 3 -5 1 1

  13. Synthetic Division Divide x4 – 10x2 – 2x + 4 by x + 3 1 0 -10 -2 4 -3 -3 +9 -3 3 -1 1 1 1 -3

  14. Homework • Page 87 #1 – 25 odd • Page 88 #1 – 13 odd, 16

  15. Page 87

  16. Page 87 A polynomial f and a factor of f are given. Factor f completely.

  17. A polynomial f and one zero of f are given. Find the other zeros of f.

  18. 25. Geometry The volume of the box shown at the right is given by V = 2x3 – 11x2 + 10x + 8 Find an expression for the missing dimension.

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