Station 14
A Problem!

Okay. Now that we are feeling really good about doing advanced algebra, I have a confession to make.

I’ve been fooling you!

Let’s go!

Question 1

Do you see that I have been avoiding negative numbers all this time?

Can we solve a problem like this one: $\dfrac {x^{3}-3x+2} {x+2}$ ?

Do you see any groups of $x+2$ in the picture?

We are looking for one dot next to two dots in the picture of $x^{3}-3x+2$ . I don’t see any.

So what can we do, besides weep a little?

Do you have any ideas? Is there anything on the app that will help?

Here’s the picture again.
I6S14-image123

It is tempting to say that we should just unexplode some dots. That’s a brilliant idea! Except ... we don’t know the value for x and so don’t know how many dots to draw when we unexplode. Bother!

We need some amazing flash of insight for something clever to do. Or maybe polynomial problems with negative numbers just can’t be solved with this dots and boxes method.

What do you think? Any ideas?