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sierranowe2003
04.07.2019 •
Mathematics
What is the result of dividing 2x^3+x^2−2x+8 by x + 2
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Ответ:
The answer is 2x² - 3x +4
Step-by-step explanation:
2x³+x²-2x+8 / x+2
= (x+2) (2x²-3x+4) / x+2
eliminate x+2
= 2x² - 3x +4
Ответ:
So for this, I will be using synthetic division. To set this up, take the root of the divisor (x + 2) and put it on one end, and then take the coefficients of the dividend (2x³ + x² - 2x + 8) and put it on the other end.
![x+2=0\\x=-2](/tpl/images/0048/8523/57064.png)
-2 | 2 + 1 - 2 + 8____________Now our division is set up. Firstly, drop the 2:
-2 | 2 + 1 - 2 + 8 ↓____________ 2Next, multiply -2 and 2, then add the product with 1:
-2 | 2 + 1 - 2 + 8 ↓ - 4____________ 2 - 3Next, multiply -2 and -3, then add the product with -2:
-2 | 2 + 1 - 2 + 8 ↓ - 4 + 6____________ 2 - 3 + 4Next, multiply 4 and -2, then add the product with 8:
-2 | 2 + 1 - 2 + 8 ↓ - 4 + 6 - 8____________ 2 - 3 + 4 + 0Now, we have just solved for the coefficients and constants. Since the dividend has a degree of 3, this means that our quotient has a degree of 2. With this info, this makes our final 2x² - 3x + 4
Ответ: