Divide (6x^2 + 5x - 4) ÷ (2x - 1) Step by Step

Step by step

The question

Question: divide (6x² + 5x − 4) by (2x − 1).

6x² + 5x − 42x − 1

1 Set it up

We write it like long division with numbers.

2x − 1 goes outside, 6x² + 5x − 4 inside.

2 First part of the answer

Divide the first parts: 6x² divided by 2x is 3x.

We write it on top.

Multiply: 3x times (2x − 1) is 6x² − 3x.

We write it under, with a minus: we take it away.

6x² take away 6x² is 0.

That is why we chose 3x.

5x take away −3x is 8x.

Bring down the next part: −4.

3 Second part of the answer

Divide the first parts: 8x divided by 2x is 4.

We write it on top.

Multiply: 4 times (2x − 1) is 8x − 4.

We write it under, with a minus: we take it away.

8x take away 8x is 0.

That is why we chose 4.

−4 take away −4 is 0.

The last part is 0.

So nothing is left over.

So the answer is 3x + 4.

Nothing is left over.

6x² + 5x − 42x − 1 = 3x + 4

4 Check

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

First the start: 6x² + 5x − 4.

Start: 6(2)² + 5(2) − 4 = 24 + 10 − 4 = 30

Now the answer: (2x − 1) times (3x + 4).

Answer: (2(2) − 1) × (3(2) + 4)

= (3) × (10) = 30

Both give 30.

So the answer is right!

Both give 30

Let's look back.

First: set it up.

Then: first part of the answer.

Then: second part of the answer.

Last: check.

Answer