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So what do we do with something like: |
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X2 + 4X = 0 |
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| X 2 and X are not the same thing. | ||
| We can't just combine them together. | ||
| BUT, what we can do is something called factoring. | ||
| What's that? | ||
| Well you know that X times X equals X 2. | ||
| and also X times 4 equals 4X so: | ||
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X times (X + 4) equals X2 + 4X |
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| STOP! TIME OUT! WHOA! HOLD ON! | ||
| Let's go through that one more time in slow motion ... | ||
| OK, OK. | ||
| If we multiply 6 times 12, | ||
| what do we actually do? | ||
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| First we multiply the 6 times the 2 | ||
| and write that down. | ||
| Then we multiply the 6 times the 10 | ||
| and write that down. | ||
| The 12 is like a 10 plus a 2. | ||
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| Then we add the 12 and the 60 | ||
| and get 72 ... | ||
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| OK, that one we know. | ||
| Now we have X + 4 times X | ||
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| We multiply X times X and write that down. | ||
| Then we multiply the X times 4 and write that down. | ||
| Then we add those two together ... | ||
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| It's a little tougher to start with X 2 + 4X | ||
| and figure out what we multiplied together to get it. | ||
| But hey, we're big shot algebra types now, | ||
| we can handle it! | ||
| That means we can rewrite: | ||
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X2 + 4X = 0 as X(X + 4) = 0 |
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| Great, just what does THAT get us? | ||
| Well, it's like this, | ||
| if you multiply two things together and get zero | ||
| then one or the other of the things | ||
| MUST be equal to zero. | ||
| So in X(X + 4) = 0 we know that either | ||
| X = 0 or X + 4 = 0 | ||
| For the X = 0 part, there's nothing to do. | ||
| X = 0 and that's that. | ||
| But we need to do a little work | ||
| to find X when we have X + 4 = 0. | ||
| It's an easy one ... | ||
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| So our two answers are X = 0 and X = -4. | ||
| Either one of those numbers could be put in place of X | ||
| in the equation ... | ||
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X2 + 4X = 0 |
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| and the thing would be true. | ||
| Let's check and see ... | ||
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| Since the terms we get at the end | ||
| on each side of the = ARE equal to each other | ||
| the answers we are testing do work. | ||
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copyright 2005 Bruce Kirkpatrick |
