# 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.

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}