Synthetic (x^3 - 2x^2 - 5x + 6) ÷ (x - 3)

Step by step

The question

Question: divide (x³ − 2x² − 5x + 6) by (x − 3).

1 Write the numbers

x − 3 is 0 when x is 3.

So we use 3.

Then we write just the numbers in front: 1, −2, −5, 6.

2 Bring down the first

The first number comes straight down: 1.

3 Times 3, then add

1 times 3 is 3.

Write it under the next number.

Add: −2 + 3 is 1.

1 times 3 is 3.

Write it under the next number.

Add: −5 + 3 is −2.

−2 times 3 is −6.

Write it under the next number.

Add: 6 + (−6) is 0.

4 Read the answer

The last number is the remainder: 0.

The other numbers are the answer's numbers: 1, 1, −2.

The answer starts one power lower than x³.

So the answer is x² + x − 2.

Nothing is left over.

5 Check

Let's check with a number: x = 2.

First the start: x³ − 2x² − 5x + 6.

Now the answer: (x − 3) times (x² + x − 2).

Both give −4.

So the answer is right!

Let's look back.

First: write the numbers.

Then: bring down the first.

Then: times 3, then add.

Then: read the answer.

Last: check.