Algebra: Introducing Polynomials
So far, most of the simplifying you've had to do has been pretty basic. For example, in Encountering Expressions, you learned exponential laws, which taught you that the product (2x4)(3x7) is equal to 2 · 3 · x4 + 7 = 6x11. In Solving Basic Equations, when you learned to solve equations, you may have manipulated the equation 3x = 9 + 2x by subtracting 2x from both sides to get x = 9. What you didn't know was that in both cases, you were actually simplifying polynomial expressions.
I haven't made a big deal about defining polynomials or gone into a lot of detail about the mechanics of simplifying such expressions so far, mainly because the sorts of things you've done to this point feel good intuitively—they sort of make sense. Sure, 5x + 9x should equal 14x; that feels right. However, before you go any farther, I want to tie up any loose ends and get specific about what kinds of things you can and can't add together, and even explore some complicated topics, like dividing variable expressions.
Excerpted from The Complete Idiot's Guide to Algebra © 2004 by W. Michael Kelley. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.