Day 2 Problems 112806

1
Day 2 Problems11/28/06

• Simplify.
• 1. 2.
• 3. 4.
• 5.

2
Synthetic Division

• Synthetic Division simpler process for dividing
  a polynomial by a binomial.
• Steps
• Write the terms of the dividend so that the
  degrees of the terms are in descending order.
  Then write just the coefficients.
• Write the constant r of the divisor x r to the
  left.
• Multiply the first coefficient by 4. Write the
  product under the second coefficient. Then add
  the product and the second coefficient.
• Multiply the sum by r. Write the product under
  the next coefficient and add.
• Multiply the sum by r. Write the product under
  the next coefficient and add. Do this until your
  remainder is 0.

3
Synthetic Division

• Use synthetic division to find (5x3 13x2 10x
  8) (x 2).
• Step 1 5x3 13x2 10x 8
• 5 -13
  10 -8
• Step 2 2 5 -13 10 -8
• ___________10____-6___8____
• Steps 3, 4, and 5 5 -3 4 0
• The numbers along the bottom row are the
  coefficients of the quotient. Start with the
  power if x that is one less than the degree of
  the dividend.
• Solution 5x2 3x 4

4
Divisor with First Coefficient Other than 1

• (8x4 4x2 x 4) (2x 1)
• Use division to rewrite the divisor so it has a
  first coefficient of 1.
• (8x4 4x2 x 4) 2 4x4 2x2 ½x 2
• (2x 1) 2 x ½
• -½ 4 0 -2 ½ 2
• -2 1 ½ -½
• 4 -2 -1 1 3/2
• The result is 4x3 2x2 - x 1 3/2
• 
  x ½
• Solution 4x3 2x2 x 1 3
• 2x 1

5
More Practice!!!

• Textbook p. 236 15 35 odd, p. 237 21- 28
• Homework worksheet 5.3 pick 11 problems