Polynomials

by
K. D.  Stroyan
University of Iowa

copyright 1997 by Academic Press, Inc. - All rights reserved.

Notebook Overview

This NoteBook has some basic algebra of polynomials.

Polynomials are functions of the form

for a sequence of constants, ((Subscript[a, 0]) ,  (Subscript[a, 1]),  (Subscript[a, 2]),  (Subscript[a, 3]),  ⋯ ,  (Subscript[a, n]))
         times integer powers of the independent variable (x in this case).  For example:

References to the Text

This NoteBook goes with Chapter 28 of the text on High School Review.

Step-by-step through Exercise 28.2.1

a

Use the mouse to put the insert bar in the next cell.  Click once and then press <Shift>+<return> or <Enter> on the number pad.  Mathematica will combine the like powers.

\(Clear[x]; 
\((6\ x\^2 + 3\ x + 7)\) + \((10\ x\^2 - 2\ x + 12)\)\)

b

Use the mouse to put the insert bar in the next cell.  Click once and then press <Shift>+<return> or <Enter> on the number pad.  Mathematica will combine the like powers.

(-7 (x^3) + (x^2) + 5 x + 1) - (3 (x^2) + 2 x - 4)

c

Mathematica can multiply polynomials, but you need to tell it to do this, because sometimes the factored expression is more useful.  Move the insert bar into the next cell click once and then enter the computation by pressing <Shift>+<Return> or number pad <Enter>.

(2  x + 1) (x + 6)Expand[(2  x + 1) (x + 6)]

d, e, f

Verify your paper and pencil work on the following:

d

(x + 7) (x - 7)

e

(3  x - 4) (x + 8)

f

(x + 1) (x - 1) (x + 2)

Computer Exercises

Mathematica can also factor.  Enter the next two computations.

Factor[-90 - 237 x - 169 (x^2) - 16 (x^3) + 12 (x^4)]

Expand[(2  x  +  3)^2 (3  x + 2) (x - 5)]