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