Return to the Purplemath home page

 The Purplemath Forums
Helping students gain understanding
and self-confidence in algebra


powered by FreeFind

 

Return to the Lessons Index  | Do the Lessons in Order  |  Get "Purplemath on CD" for offline use  |  Print-friendly page

Evaluation: Evaluating
    Expressions, Polynomials, and Functions
(page 1 of 2)

Sections: Evaluating Expressions and Polynomials, Evaluating Functions


"Evaluation" mostly means "simplifying an expression down to a single numerical value". Sometimes you will be given a numerical expression, where all you have to do is simplify; that is more of an order-of-operations kind of question. In this lesson, I'll concentrate on the "plug and chug" aspect of evaluation: plugging in values for variables, and "chugging" my way to the simplified answer.

Usually the only hard part in evaluation is in keeping track of the minus signs. I would strongly recommend that you use parentheses liberally, especially when you're just getting started.

  • Evaluate a2b for a = 2, b = 3, c = 4, and d = 4.

    To find my answer, I just plug in the given values, being careful to use parentheses, particularly around the minus signs:   Copyright Elizabeth Stapel 2000-2011 All Rights Reserved

      (2)2(3) = (4)(3) = 12

  • Evaluate a cd for a = 2, b = 3, c = 4, and d = 4.
    • (2) (4)(4) = 2 (16) = 2 + 16 = 16 2 = 14

  • Evaluate (b + d)2 for a = 2, b = 3, c = 4, and d = 4.

    I must take care not to try to "distribute" the exponent through the parentheses. Exponents do NOT distribute over addition! I should never try to say that (b + d)2 is the same as b2 + d2! They are NOT the same thing! I must evaluate the expression as it stands:

      ( (3) + (4) )2 = ( 7 )2 = 49

  • Evaluate b2 + d2 for a = 2, b = 3, c = 4, and d = 4.
    • (3)2 + (4)2 = 9 + 16 = 25

Notice that this does not match the answer to the previous evaluation, pointing out again that exponents do not "distribute" the way multiplication does.

  • Evaluate bc3 ad for a = 2, b = 3, c = 4, and d = 4.
    • (3)(4)3 (2)(4) = (3)(64) (8) = 192 + 8 = 184


The most common "expression" you'll likely need to evaluate will be polynomials. To evaluate, you take the polynomial and plug in a value for x.

  • Evaluate x4 + 3x3 x2 + 6 for x = 3.
    • (3)4 + 3(3)3 (3)2 + 6
          = 81 + 3(27) (9) + 6
          = 81 81 9 + 6
          = 3

  • Evaluate 3x2 12x + 4 for x = 2.
    • 3(2)2 12(2) + 4 = 3(4) + 24 + 4 = 12 + 24 + 4 = 40

  • Evaluate y = 4x 3 at x = 1.
    • y = 4(1) 3 = 4 3 = 7

    Note: This means that the point (1, 7) is on the line y = 4x 3.


You can use the Mathway widget below to practice "Simplifying and Evaluating Expressions", subtopic "Evaluating Expressions". Try the entered exercise, or type in your own exercise. Then click "Answer" to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)

(Clicking on "View Steps" on the widget's answer screen will take you to the Mathway site, where you can register for a free seven-day trial of the software.)

Top  |  1 | 2  | Return to Index  Next >>

Cite this article as:

Stapel, Elizabeth. "Evaluation: Expressions and Polynomials." Purplemath. Available from
    http://www.purplemath.com/modules/evaluate.htm. Accessed
 

 



Purplemath:
  Linking to this site
  Printing pages
  School licensing


Reviews of
Internet Sites:
   Free Help
   Practice
   Et Cetera

The "Homework
   Guidelines"

Study Skills Survey

Tutoring from Purplemath
Find a local math tutor


This lesson may be printed out for your personal use.

Content copyright protected by Copyscape website plagiarism search

  Copyright 2000-2012  Elizabeth Stapel   |   About   |   Terms of Use

 

 Feedback   |   Error?