5.1 – 5.3 Review
Name:_________________________________
Perform the indicated operation.
1. (–6x2 + 5x – 2) – (7x2 – 5x – 8)
2. (𝑎2 − 𝑏 + 𝑐)(𝑏 − 𝑐)
3. 2 x  y 2 x  y 
4. Use synthetic division to divide (5x4  2x2 + 1)  (x + 1)
5. Use long division to divide 2x3 + 7x2 – 3x – 20 by x2 + x – 4.
6. Complete the chart. Given the characteristics of each polynomial function, describe the end behavior.
Characteristics of the graph of a polynomial function
Left End Behavior
as x  
Right End Behavior
as x  
a. A 5th degree polynomial with a negative leading coefficient.
b. A 6th degree trinomial with a positive leading coefficient.
c. A Quartic monomial with a negative leading coefficient.
d. A 79th degree polynomial with a positive leading coefficient.
7. Which term of a polynomial function is most important in determining the end behavior of the function?
8. What is the greatest number of local maximums and minimums that a quartic function can have?
9. Use as many terms as you can to describe the polynomial function,
f ( x)  4 x3  2 x 2  x  11
Use Properties of exponents to simplify the expressions.
4

9
2
10. 
11. 70 ∙ 5-3
3 6 -2
13. (3x y )
16.
2
1


2 2 2
 2 x y  
2 5 2

  x y 


1 3
2 3 2
 3xy  x y    x 2 y 3 


 


 
2 -3
12. (82 ∙ 8-3)2 ∙ 82
2
14. (x y )(xy )
 2x 
15.  2 
y 
3