6-3 Dividing Polynomials
Example #1: Polynomial Long Division
a)   x3  3x 2  6    x 2  1
b)
 2x
4
 x3  x 2  x    2 x  1
c)  2 x 2  13x  15   x  5
Example #2 – Checking Factors
Use division to determine whether  x  4  is a factor of each polynomial. Explain your answer.
a) x2  6 x  8
b) x3  3x2  6 x  7
Example #3 – Using Synthetic Division
Use synthetic division to divide the following.
a)  3x3  4 x 2  2 x  1   x  1
c) Is
b)
x
3
 x  2
a factor of  x3  4 x 2  3x  2  ?
 4 x 2  x  6    x  3
When would you choose to use long division instead of synthetic division?
Example #4
Given  x  2  is a factor of  x3  2 x 2  5x  6  , find the remaining factors.
Example #5 – Evaluating a Polynomial using Synthetic Division
Use substitution to evaluate…
a) P  4 given P( x)  x4  5x2  4 x  12
b) 2 x4  6 x3  5x2  60 at x = -1
Use synthetic division to evaluate…
a) P  4 given P( x)  x4  5x2  4 x  12
b) 2 x4  6 x3  5x2  60 at x = -1