Opener
Simplify
3x 3
1. 2
x
Find the missing factor
2
2.
5-4 Dividing Polynomials
Divide
5x
x2
3. x 2  2x  63   x  9
4. 2x 2  13x  15   x  5
52 3 7 5 2 5
Example:
Divide 2x 4  3x 3  5x  1 by x 2  2x  2
Try:
f  x   3x 3  2x 2  2x  5 divided by x  2


Synthetic Division
** only use when the divisor is
** Write the
** Divisor is
f  x   3x 3  2x 2  2x  5 divided by x  2
Factor Theorem:
Checking Factors
Step 1:
Step 2:
Example:
Is x – 2 a factor of P  x   x 5  32 ? If it is, write P  x  as a product of two factors.
Example:
Is x 2  1 a factor of 3x 4  4 x 3  12x2  5 ?
Remainder Theorem:
Evaluating a Polynomial
Given that P  x   x 5  2x 3  x 2  2 , what is P  3 ?
Divide x 3  2x2  6x  9 by x  3 . What is the remainder?
Factor f  x   2x 3  11x 2  18x  9 given that f  3  0
What if the directions say to solve the previous problem?
Use Synthetic Division to Solve a Problem
CRAFTS: The polynomial x 3  7x2  38x  240 expresses the volume,
in cubic inches, of the shadow box shown.
A. What are the dimensions if the box?
(Hint: the length is greater than the height (or depth))
B. If the width of the box is 15 in., what are the other two dimensions?
Assignment: p.308 22-38 even, 46-48, 53-56