Question

Use synthetic division to find the result when the polynomial x^3 - 2x^2 + 2x + 5 is divided by a specific divisor or term. Please provide the divisor or term you would like to use in the synthetic division.

Answer 1

To divide the polynomial x^3 - 2x^2 + 2x + 5 by a specific divisor using synthetic division, set up a synthetic division table and perform the division step-by-step. The result of the division is x^2 - 2x + 6 with a remainder of 11.

Step-by-step explanation:

To perform synthetic division, we need to choose a specific divisor or term. Let's choose the divisor 2. So the polynomial we want to divide is x^3 - 2x^2 + 2x + 5 and the divisor is 2.

The first step is to set up the synthetic division table. Write down the coefficients of the polynomial in descending order:

1 -2 2 5

Next, bring down the first coefficient, which is 1. Multiply it by the divisor 2 and write the result beneath the next coefficient:

2

1 -2 2 5

2

Add the two numbers in the second column and write the result:

1 -2 2 5

2 -2

Repeat the process, multiplying -2 by 2 and writing the result beneath the next coefficient:

1 -2 2 5

2 -2

4

Add the two numbers in the third column and write the result:

1 -2 2 5

2 -2 6

Add the final result, 6, to the last coefficient, 5:

1 -2 2 5

2 -2 6 11

The result of the division is x^2 - 2x + 6 with a remainder of 11.