Synthetic Division...B

[nycmathguy]

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.

 

[MathLover1]

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,

 

[nycmathguy]

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.
View attachment 2804

Step 1

Write down the first coefficient without changes:

View attachment 2805
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.

View attachment 2806
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.

View attachment 2807
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.
View attachment 2808

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, View attachment 2809

This is not your typical synthetic division classroom test problem.