Evaluation:
Evaluating 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 orderofoperations 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.
To find my answer, I just plug in the given values, being careful to use parentheses, particularly around the minus signs: Copyright © Elizabeth Stapel 20002011 All Rights Reserved (–2)^{2}(3) = (4)(3) = 12
(–2) – (–4)(4) = –2 – (–16) = –2 + 16 = 16 – 2 = 14
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 b^{2} + d^{2}! They are NOT the same thing! I must evaluate the expression as it stands: ( (3) + (4) )^{2} = ( 7 )^{2} = 49
(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.
(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.
(–3)^{4} + 3(–3)^{3} – (–3)^{2} + 6
3(–2)^{2} – 12(–2) + 4 = 3(4) + 24 + 4 = 12 + 24 + 4 = 40
y = 4(–1) – 3 = –4 – 3 = –7 Note: This means that the point (–1, –7) is on the line y = 4x – 3.
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