Synthetic (x^2 - 9x + 20) ÷ (x - 5)

Step by step

The question

Question: divide (x² − 9x + 20) by (x − 5).

1 Write the numbers

x − 5 is 0 when x is 5.

So we use 5.

Then we write just the numbers in front: 1, −9, 20.

2 Bring down the first

The first number comes straight down: 1.

3 Times 5, then add

1 times 5 is 5.

Write it under the next number.

Add: −9 + 5 is −4.

−4 times 5 is −20.

Write it under the next number.

Add: 20 + (−20) is 0.

4 Read the answer

The last number is the remainder: 0.

The other numbers are the answer's numbers: 1, −4.

The answer starts one power lower than x².

So the answer is x − 4.

Nothing is left over.

5 Check

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

First the start: x² − 9x + 20.

Now the answer: (x − 5) times (x − 4).

Both give 6.

So the answer is right!

Let's look back.

First: write the numbers.

Then: bring down the first.

Then: times 5, then add.

Then: read the answer.

Last: check.