Step by step
The question
Question: divide (2x³ + x² − 7x − 6) by (2x + 3).
1 Set it up
We write it like long division with numbers.
2x + 3 goes outside, 2x³ + x² − 7x − 6 inside.
2 First part of the answer
Divide the first parts: 2x³ divided by 2x is x².
We write it on top.
Multiply: x² times (2x + 3) is 2x³ + 3x².
We write it under, with a minus: we take it away.
2x³ take away 2x³ is 0.
That is why we chose x².
x² take away 3x² is −2x².
Bring down the next part: −7x.
3 Second part of the answer
Divide the first parts: −2x² divided by 2x is −x.
We write it on top.
Multiply: −x times (2x + 3) is −2x² − 3x.
We write it under, with a minus: we take it away.
−2x² take away −2x² is 0.
That is why we chose −x.
−7x take away −3x is −4x.
Bring down the next part: −6.
4 Third part of the answer
Divide the first parts: −4x divided by 2x is −2.
We write it on top.
Multiply: −2 times (2x + 3) is −4x − 6.
We write it under, with a minus: we take it away.
−4x take away −4x 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: 2x³ + x² − 7x − 6.
Now the answer: (2x + 3) times (x² − x − 2).
Both give 0.
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.