# Synthetic Division...B

Discussion in 'Algebra' started by nycmathguy, Apr 27, 2022.

1. ### nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
422
College Algebra
Section R.8

138. Use synthetic division to determine if
x - (1 + sqrt{2}) is a factor of x^3 - 9x^2 + 13x + 7.

nycmathguy, Apr 27, 2022
2. ### MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,884
Take the constant term of the divisor with the opposite sign and write it to the left.
Write the coefficients of the dividend to the right.

Step 1

Write down the first coefficient without changes:

Step 2

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Step 3

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Step 4

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

We have completed the table and have obtained the following resulting coefficients:

1,−8+sqrt(2),7−7sqrt(2),0

All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus, the quotient is x^2+x(−8+sqrt(2))+7−7sqrt(2), and the remainder is 0.

Therefore,

MathLover1, Apr 27, 2022
nycmathguy likes this.

Joined:
Jun 27, 2021
Messages:
5,386