29 lines
1.6 KiB
Markdown
29 lines
1.6 KiB
Markdown
---
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title: Definition of Factor
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---
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## Definition of Factor
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Factors are two numbers that we can multiply together to yield another number.
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For example, 2 * 10 = 20, so 2 and 10 are factors of 20.
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Often in algebra, we want to factor out expressions.
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Take, (x^2 + 4x +3), in the form Ax^2+Bx+C
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in order to factor this by looking for two numbers that will multiply to equal C and add up to equal C.
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3 and 4 add up to 4 and multiply to equal 3.
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With this in mind, (x^2 + 4x +3) can be factored out into (x+3)(x+1).
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A factor can be defined in 2 ways. The first is in multiplication. Take _3 * 4 = 12_. Here _3_ and _4_ are factors, and together they make a product. Another way a factor can be defined is if the remainder upon division equals 0. Take the number 12. If we divide 12 by 4
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_12 / 4 = 3_
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The remainder is 0. There are no decimal spaces, and therefore 4 is _a factor of_ 12. Likewise, if we do
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_12 / 3 = 4_
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we also get a remainder of 0. Therefore both 3 and 4 are factors of 12.
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We can simplify this and use _%_ as the modulo function. This will give us
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_12 % 3 = 0_
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Because the modulo function returns the remainder upon division, any number that returns 0 upon the use of modulo is a factor of the other number.
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#### More Information:
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[Here's a link](https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-factors-mult/v/finding-factors-of-a-number) to a quick video explaining factoring numbers
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Learn more about factoring out expressions [here](https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-factors-mult/v/finding-factors-and-multiples)
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