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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.)

To activate, click in the "Enter Problem" box below:

(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.)

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