College Algebra
Answer/Discussion to Practice Problems
Tutorial 37:Synthetic Division and
the Remainder and Factor Theorems
Answer/Discussion
to 1a

Synthetic division would look like this:


*(1)(4) = 4
*Place 4 in next column

The numbers in the last row make up your coefficients of the quotient
as well as the remainder. The final value on the right is the remainder.
Working right to left, the next number is your constant, the next is the
coefficient for x, the next is the coefficient
for x squared, etc...

Answer/Discussion
to 2a

Using synthetic division to find the remainder we get:
Again, our answer this time is not a quotient, but the remainder.
Final answer: f(1) = 9 
Answer/Discussion
to 3a

Using synthetic division to find the quotient we get:
Note how the remainder is 0. This means that (x  1/2) is a factor of . 
Rewriting f(x)
as (x  1/2)(quotient) we get:
We need to finish this problem by setting this equal to zero and
solving it: 
The solution or zeros of this function are x = 1/2, 2, and 2. 
Last revised on March 15, 2010 by Kim Seward.
All contents copyright (C) 2002  2012, WTAMU and Kim Seward. All rights reserved.

