Step by step
The question
Question: divide (x³ − 2x² − 5x + 6) by (x − 3).
1 Set it up
We write it like long division with numbers.
x − 3 goes outside, x³ − 2x² − 5x + 6 inside.
2 First part of the answer
Divide the first parts: x³ divided by x is x².
We write it on top.
Multiply: x² times (x − 3) is x³ − 3x².
We write it under, with a minus: we take it away.
x³ take away x³ is 0.
That is why we chose x².
−2x² take away −3x² is x².
Bring down the next part: −5x.
3 Second part of the answer
Divide the first parts: x² divided by x is x.
We write it on top.
Multiply: x times (x − 3) is x² − 3x.
We write it under, with a minus: we take it away.
x² take away x² is 0.
That is why we chose x.
−5x take away −3x is −2x.
Bring down the next part: 6.
4 Third part of the answer
Divide the first parts: −2x divided by x is −2.
We write it on top.
Multiply: −2 times (x − 3) is −2x + 6.
We write it under, with a minus: we take it away.
−2x take away −2x is 0.
That is why we chose −2.
6 take away 6 is 0.
The last part is 0.
So nothing is left over.
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: set it up.
Then: first part of the answer.
Then: second part of the answer.
Then: third part of the answer.
Last: check.