SaiBook.us Algebra

Example

Title: Synthetic division

Grade: 8-a Lesson: S1-L4

Explanation: The best way to understand algebra is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

Divide \$(x^3 - 1)\$ by \$(x - 1)\$ using synthetic division.

Step 1a

$1a$

Explanation: Write the problem in synthetic division format.

Step 1b

$1b$

Explanation: Carry down the leading coefficient, unchanged, to below the division symbol.

Step 1c

$1c$

Explanation: Multiply the carry-down value by the zero of the denominator, and carry the result up into the next column 1 . 1 = 1.

Step 1d

$1d$

Explanation: Add down the column: 0 + 1 = 1.

Step 1e

$1e$

Explanation: Multiply the carry-down value by the zero of the denominator, and carry the result up into the next column 1 . 1 = 1.

Step 1f

$1f$

Explanation: Add down the column: 0 + 1 = 1.

Step 1g

$1g$

Explanation: Multiply the carry-down value by the zero of the denominator, and carry the result up into the next column 1 . 1 = 1.

Step 1h

$1h$

Explanation: Add down the column: -1 + 1 = 0. The last carry-down value is the remainder 0.

Step 1i

Write the result in polynomial format: \$ x^2 + x + 1 \$.

Explanation: Therefore, the polynomial format is \$ x^2 + x + 1 \$.