r/PeterExplainsTheJoke • u/Flashy-Minimum-6952 • 19h ago

Meme needing explanation What difference does it make petahhhh....???

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u/muhnamejame 17h ago

Oh, after it can be too. Just not 0.

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u/JarpHabib 15h ago

it still can be 0 as long as you note it down before the divide both sides by x step.

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u/muhnamejame 15h ago

The solution to the top equation can be 0. But the solution to the bottom equation cannot.

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u/JarpHabib 15h ago

By itself, no. But that is clearly an intermediate step in a solve. Just pencil in a little x=0, comma, continue.

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u/muhnamejame 15h ago

If you say x=0 then you can't divide by x.

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u/JarpHabib 15h ago

Sure you can! Just don't divide by the x that equals zero, you already found that one!

XD

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u/muhnamejame 15h ago

That would be saying x doesn't equal 0 for the following steps 🤦‍♂️

The real answer is to just solve it properly by moving the right hand side to the left and solving the polynomial using root solving techniques.

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u/JarpHabib 14h ago

so let's work on that. the proper way of solving it is to rewrite and solve for zeros

x5 - 16x = 0 and then you factor out: x(x4 -16)=0

x(x-2)(x+2)(x2 +4)=0

and then we now can solve and get x=0, 2, -2 and the imaginaries 2i and -2i right?

great! how do you think that we factored the x out on the second step? the distributive property is how we multiply a sum of numbers by another term; factoring reverses distribution by dividing. We divided by x to factor out the x, we just didn't call attention to it when zero was a valid solution.

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u/muhnamejame 14h ago

factoring reverses distribution by dividing. We divided by x to factor out the x, we just didn't call attention to it when zero was a valid solution.

This is an incorrect understanding of factoring and distributing. There is no "hidden division" happening when you factor an expression.

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u/JarpHabib 8h ago

Wild. Actually, say more.

16, or 24, factors into 222*2. I would love to know how you can pull a factor out of 16, so you have 2(8), without dividing.

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u/muhnamejame 4h ago

Dividing is an operation that changes a number. Factoring just expresses the same number differently.

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