Work Text:
The equation playground, its green grass and blue sky as always, but more importantly are all the algebralians hanging around with each other, giving the place a bustling and joyful atmosphere.
Four was frolicking happily around, singing his usual tune until he noticed X, who once again sat depressingly against the base of a tree.
He approaches the variable and asks, "X! What's wrong? You look... woebegone!"
"Well... Ever since I got this exponent, everything's felt like a roller coaster of emotions! I don't want it anymore, Four, do you know how to get rid of it?"
The number sat down in front, noticing the green bit hanging on top of X, he thought for a bit, "Then... Let's head to the equation playground!"
[*Radio Martini by Kevin MacLeod starts playing*]
So...
The two algebralians walk together amongst the see-saws with other numbers on them.
"So X, do you still remember the last time we found out your value here?"
"Um... Yeah!"
"This time we're not going to use a see-saw, we're going to use... this!"
They walk up to an elevated 2-level bench. Four continues, "X, hop on the top bench!"
As the variable sits, Four takes other numbers and variables and adds them onto the top bench. As he does, they slide around the bench and combine themselves with like-terms and simplify the expression.
Finally, he sits down next to X and tells him, "Wasn't that cool? Now we can start factoring to get rid of your exponent!"
"But Four, how are we going to do that with just this?"
4x2 + 7x - 15
"We can use the slide and divide method and with a pencil!"
"First, I'll get down for now and multiply that 15 by me, so we get 60. This is the slide part!"
x2 + 7x - 60
"On the second bench, I'll put two brackets and split you into two!"
(x )(x )
"Woah that's so cool Four!"
"Thanks! Now X, this is the hardest part! Can you think of 2 numbers that add to 7 and multiply to negative 60?"
"Umm... I don't think so..."
"Don't worry X I'll get you through this! If two numbers multiply and the product is negative, that means one of the two numbers has to be negative! But not both of them because then the product would have to be positive!"
"Oh... Why's it like that, Four..." This made X even more confused.
"Well, it's like if you turn around, you'll face the other way! If you turn twice, you're back where you started!"
"Ohhhh! I understand now!"
"Anyways, because this part is pretty hard, we can use the help of a friend!"
"Who is it, Four?"
"It's the Factor Finder! We can give it a number and most of the time it could generate kind of a times table for that number!" He uses the pencil to duplicate the 60 and feed it into the machine. It displays:
60 x 1
30 x 2
20 x 3
15 x 4
12 x 5
10 x 6
"Wait, why didn't it make the full times table?"
"Because we don't need to! Now, which pair of numbers when you subtract the left number by the right one gives us 7?"
"Um... Oh! It's 12 and 5!"
"That's right, now we can add 12 and negative 5 to our brackets, or terms."
"Does the order we add them matter?"
"No actually! we can put the negative 5 in the first term and positive 12 in the second term!"
(x - 5)(x + 12)
"Finally, we have the divide part! Remember when I said I got off? Well, we're going to divide -5 and 12 by me! This is going to make it like a fraction!"
(x - 5/4)(x + 12/4)
"Oh! And then we simplify them! 12/4 becomes 3 and 5/4 is... 1.5?"
"No X! If we can't divide the integer without turning it into a decimal, then we have to bring it up to you as a coefficient!"
(4x - 5)(x + 3)
"Okay! What's the next step, Four?"
"There's no more steps, we're done! And look, I'm with you!"
"Yay! I feel a lot better now, thanks Four!"
They hop off the bench and walk back towards where the other numbers are playing.
"No problem, X! You're my world, I'll do anything to help you!..."
[To be continued...]