Question

complete the synthetic division problem below.-2| 2 2 -2 4what is the quotient in polynomial form?a. 2x^2+2x-2b. 2x^2+2x-4c. 2x^2-2x+4d. 2x^2-2x+2

Answer 1

`D\text{. }2x^2\text{- 2x + 2}`

Step-by-step explanation

We want to finish the synthetic division given:

-2| 2 2 -2 4

Step 1:

Drop down 2:

-2| 2 2 -2 4

|

2

Step 2: Mutliply -2 by the 2 that was dropped down:

-2| 2 2 -2 4

|+ -4

2

Step 3: Add 2 and -4:

-2| 2 2 -2 4

|+ -4

2 -2

Step 4: Repeat (2) and (3) with -2 and -2

-2| 2 2 -2 4

|+ -4 4

2 -2 2

Step 5: Repeat (2) and (3) with -2 and 2:

-2| 2 2 -2 4

|+ -4 4 -4

2 -2 2 0

It is important to note that since we started with 4 coefficients (2, 2, -2 and 4), the largest power of the expression we divided was 3 i.e.:

`2x^3+2x^2\text{ - 2x + 4}`

This means that the largest power of our quotient is 2.

So, the answer is:

`2x^2\text{- 2x + 2}`

Option D