Question

What is the result of dividing 2x^3+x^2−2x+8 by x + 2

Answer 1

The answer is 2x² - 3x +4

Explanation:

2x³+x²-2x+8 / x+2

= (x+2) (2x²-3x+4) / x+2

eliminate x+2

= 2x² - 3x +4

Answer 2

Steps:

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`

• -2 | 2 + 1 - 2 + 8
• ____________

Now our division is set up. Firstly, drop the 2:

• -2 | 2 + 1 - 2 + 8
• ↓
• ____________
• 2

Next, multiply -2 and 2, then add the product with 1:

• -2 | 2 + 1 - 2 + 8
• ↓ - 4
• ____________
• 2 - 3

Next, multiply -2 and -3, then add the product with -2:

• -2 | 2 + 1 - 2 + 8
• ↓ - 4 + 6
• ____________
• 2 - 3 + 4

Next, multiply 4 and -2, then add the product with 8:

• -2 | 2 + 1 - 2 + 8
• ↓ - 4 + 6 - 8
• ____________
• 2 - 3 + 4 + 0

Answer:

Now, 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 answer: 2x² - 3x + 4