Basic Mathematics for College Students

Find the degree of each polynomial.

13. 5 x^3 14. 3 t^5  3 t^2


14. 2 x^2  3 x 2 16.


15. 2 m 18. 7 q 5


16. 25 w^6  5 w^7 20. p^6 p^8

Complete each solution.

21. Evaluate 3a^2  2 a7 for a2.


22. Evaluate q^2  3 q2 for q1.

Evaluate each polynomial for the given value.

23. 3 x4 for x 3


24. for x 6


25. 2 x^2 4 for x 1


26. for x 2


27. 0.5t^3 1 for t 4


28. 0.75a^2 2.5a2 for a 0


29. for b 3


30. 3 n^2 n2 for n 2


31.  2 s^2  2 s1 for s 1


32.  4 r^2  3 r1 for r 2

2

3

b^2 b 1



1

2

x^2  1

1

2

x 3

PRACTICE

 4

  2

  1   2

  1 2  31  12  2

q^2  3 q 2  1 22  31 2  2

 9

  7

 12  4  7

 31 2   7

3 a^2  2 a 7  31 22  21 2  7

NOTATION

1

2

p^4 p^2

The height h (in feet) of a ball shot straight up with an

initial velocity of 64 feet per second is given by the equation

h 16t^2 64t. Find the height of the ball after the given

number of seconds.

33. 0 second 34. 1 second


34. 2 seconds 36. 4 seconds

The number of feet that a car travels before stopping depends

on the driver’s reaction time and the braking distance. For

one driver, the stopping distance d is given by the equation

d 0.04v^2 0.9v, where v is the velocity of the car. Find the

stopping distance for each of the following speeds.

37. 30 mph 38. 50 mph


38. 60 mph 40. 70 mph


39. Explain how to find the degree of the polynomial
    2 x^3  5 x^5  7 x.


40. Explain how to evaluate the polynomial  2 x^2  3
    for x5.

Perform the operations.

43. 
    
    
    
    44. 
        
    
    
    
    


44. 
    
    
    
    46. 
        
    
    
    
    

Solve each equation.

47. x 4  12 48. 4 z 108


48. 2(x3)  6 50. 3(a5) 4(a9)

23

25



46

5

5

12

#^18

5

36

7



23

7

2

3



4

3

REVIEW

WRITING

d

Decision

to stop

50 mph Reaction time Braking distance

APPLICATIONS

A-8 Appendix II Polynomials

SECTION II.2

Adding and Subtracting Polynomials

Objectives

1 Add polynomials.

2 Subtract polynomials. Polynomials can be added, subtracted, and multiplied just like numbers in arithmetic.

In this section, we show how to find sums and differences of polynomials.