Algebra 2
Section 5.2 Polynomial Long Division Day 3
Divide the following expressions using an appropriate method.
Identify if the divisor is a factor of the dividend.
1.  3 x  2 x 3  4    x  1
2. (4 x  2 x 3  7 x 2  1)  ( x  1)
3.
4 x

4.
 4x
5.
x 2  2 x 5 x 4  14 x 3  9 x
6.
6x
7.
(4 x3  2 x 2  6 x  1)  (2 x  3)
8.
4 x
3
 
 6x2  5  x 2  4
3
 2 x 2  1
(2  x )
3
3
 2 x 2  5 x  3
( x  3)

 6 x 2  4 x  1 2 x  1
1
Algebra 2
Section 5.2 Polynomial Long Division Day 3
Divide the following expressions using an appropriate method.
Identify if the divisor is a factor of the dividend.
1.
(4 x  2 x 3  7 x 2  1)  ( x  1)
2.
4 x
3.
 4x
4.
x 2  2 x 5 x 4  14 x 3  9 x
3
 2 x 2  1
(2  2 x)
3
 
 6x2  5  x 2  4
Answer the following questions and show all work.

5. A rectangular box for a new product is designed in such a way that the three dimensions
always have a particular relationship defined by the variable x. The volume of the box
can be written as 6 x 3  31x 2  53 x  30 and the height is given by x  2 . What are the width
and length of the box?
6. Kelly and Vincent are dividing f ( x)  2 x 3  4 x 2  3 x  1 by x  3 . Kelly claims the remainder
is 26 and Vincent argues the remainder is 100. Is either of them correct? Explain your
reasoning.
x3  8
7. Simplify the expression
using long division, synthetic division and factoring.
x2
Explain the pros and cons of each method.
8. Write the polynomial divisor, dividend and quotient represented by the synthetic division
below.
9. You divide two polynomials and obtain the result below. What is the divisor? What is the
dividend? Show all work to support your answer.
5 x 2  13x  47 
102
x2