Question

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

Answer 1

When `x=0," "5x-2="–"2.`
When `x="–"1," "5x-2="–"7`.

Explanation:

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

• (a) `x=0` and
• (b) `x="–"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 xx x`, written as `5x`), and then subtracts 2 (giving us `5x-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 `5x-2` when `x=0`. We do this by replacing all the `x"'s"` with `0"'s"`:

`color(white)=5x-2 color(magenta)(" at " x=0)`

`=5(0) - 2`

then we follow the order of operations, multiplying `5 xx 0` first:

`=0 - 2`

and finally subtracting 2:

`=" –2"`

So if Player 1 picks the number `0`, Player 2 will be the number `"–2".`

If we evaluate `5x-2` when `x="–1"`, we get:

`color(white)=5x-2 color(magenta)(" at " x="–"1)`

`=5("–1") - 2`

`="  ""–5""   "-2`

`=" –7"`

So if Player 1 picks the number `"–"1`, Player 2 will be the number `"–"7`.