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Masja [62]
3 years ago
13

How to use synthetic division to show how to methodically obtain the factors from the polynomial 2x^5+6x^4-42x^3-86x^2+192x+360

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
6 0
Okay so first you need to find your prrs which in this case would be all factors of 360 and all of the factors of 360 divided by two since the factors of two are two and one. (Which I pulled from the first x’s coefficient)

Then you do Descartes law to find out how many positives or negatives in this equation. There looks to be 2 positives and 3 or 0 negatives. Since there are guaranteed positives I’d recommend doing those first. Start from the lowest number since that’s easier and more mathematically correct and do synthetic division. (x+1) The resulting polynomial should be factorable and of not then try to synthetically divide again.
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The ratio of red to green is 5:6 which means that for every 5 red cars, there are 6 green cars

The ratio of green to blue is 3:10 telling us that for every 3 green cars, there are 10 blue cars. 

The ratio 3:10 is equivalent to 6:20 after we multiply both parts by 2. This now says that for every 6 green cars, there are 20 blue cars.

------------------------------

Let's say we had 5 red cars, 6 green cars and 20 blue cars
Based on that info, we know that the ratio of red to green is 5:6
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We don't reduce 6:20 to 3:10 however, since that would change the green count from 6 to 3. We want to keep the green count at 6.

So because there are 5 red cars, 6 green cars, and 20 blue cars in this example, and this example points to the proper ratios mentioned earlier, this means that the final answer is 5:6:20. This ratio cannot be reduced or simplified as there are no common factors (other than 1) for 5, 6, and 20.
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