# What do you get when you evaluate 5x-2 at both 0 and –1?

Feb 23, 2017

When $x = 0 , \text{ "5x-2="–} 2.$
When $x = \text{–"1," "5x-2="–} 7$.

#### Explanation:

Given the polynomial $5 x - 2$, we are asked to evaluate it when

• (a) $x = 0$ and
• (b) $x = \text{–} 1$.

To evaluate a polynomial like this means to work out its numeric value when its variable is fixed at a specific number.

Our polynomial takes a number $x$, multiplies it by 5 (giving us $5 \times x$, written as $5 x$), and then subtracts 2 (giving us $5 x - 2$).

It's like a two-player game. Player 1 picks a number, and it's Player 2's job to multiply that number by 5, and then subtract 2. We are Player 1, and our polynomial is Player 2.

Let's evaluate $5 x - 2$ when $x = 0$. We do this by replacing all the $x \text{'s}$ with $0 \text{'s}$:

$\textcolor{w h i t e}{=} 5 x - 2 \textcolor{m a \ge n t a}{\text{ at } x = 0}$

$= 5 \left(0\right) - 2$

then we follow the order of operations, multiplying $5 \times 0$ first:

$= 0 - 2$

and finally subtracting 2:

$= \text{ –2}$

So if Player 1 picks the number $0$, Player 2 will be the number $\text{–2} .$

If we evaluate $5 x - 2$ when $x = \text{–1}$, we get:

$\textcolor{w h i t e}{=} 5 x - 2 \textcolor{m a \ge n t a}{\text{ at " x="–} 1}$

$= 5 \left(\text{–1}\right) - 2$

$= \text{ ""–5"" } - 2$

$= \text{ –7}$

So if Player 1 picks the number $\text{–} 1$, Player 2 will be the number $\text{–} 7$.