Evaluate the expression x^4 - 2x^3 + 5x^2 + 10x + 12 for x = 2.

Question:

Evaluate the expression

{eq}x^4 - 2x^3 + 5x^2 + 10x + 12 {/eq}

for {eq}x = 2 {/eq}.

Evaluating an Expression at a Value:

To evaluate an expression that is in terms of one or more variables at given values of variables, we just simplify the values of the variables in the given expression and simplify it.

Answer and Explanation:

The given expression is:

$$x^4 - 2x^3 + 5x^2 + 10x + 12 $$

We substitute {eq}x=2 {/eq} here:

$$\begin{align} 2^4 - 2(2^3) + 5(2^2) + 10(2) + 12&= 16 - 16 + 20 +20 +12 \\ & = 0+20+20+12 & (\because 16-16=0)\\ &= \boxed{\mathbf{52}} \end{align} $$


Learn more about this topic:

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Evaluating Simple Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 3
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