Synthetic Division...A

[nycmathguy]

College Algebra
Section R.8

137. Use synthetic division to find the quotient and remainder when x^3 - 4x^2 - 3x + 13 is divided by x - cuberoot{3}.

 

[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:

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

Thus, the quotient is

, and the remainder is

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 2810


Step 1

Write down the first coefficient without changes:

View attachment 2811

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 2812


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 2813


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 2814

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

View attachment 2815

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

Thus, the quotient is View attachment 2816, and the remainder is View attachment 2817


Therefore, View attachment 2819=

View attachment 2818

Wow! This is synthetic division at a different level.