Step by step
The question
Question: divide (3x² − 10x + 3) by (x − 3).
1 Set it up
We write it like long division with numbers.
x − 3 goes outside, 3x² − 10x + 3 inside.
2 First part of the answer
Divide the first parts: 3x² divided by x is 3x.
We write it on top.
Multiply: 3x times (x − 3) is 3x² − 9x.
We write it under, with a minus: we take it away.
3x² take away 3x² is 0.
That is why we chose 3x.
−10x take away −9x is −x.
Bring down the next part: 3.
3 Second part of the answer
Divide the first parts: −x divided by x is −1.
We write it on top.
Multiply: −1 times (x − 3) is −x + 3.
We write it under, with a minus: we take it away.
−x take away −x is 0.
That is why we chose −1.
3 take away 3 is 0.
The last part is 0.
So nothing is left over.
So the answer is 3x − 1.
Nothing is left over.
4 Check
Let's check with a number: x = 2.
First the start: 3x² − 10x + 3.
Now the answer: (x − 3) times (3x − 1).
Both give −5.
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.
Last: check.