# Long Division

How to do the long division to divide a polynomial by a binomial: 1 example and its solution.

## Example

### Example

### Solution

Just like dividing numbers,

draw the division form like this.

Write the dividend (x^{2} + 3x - 10) in the form.

And write the divisor (x - 2) in the left side of the form.

The goal is to remove x^{2} of (x^{2} + 3x - 10)

by using the divisor (x - 2).

You can make x^{2} by multiplying (x - 2) and x.

So write x in the quotient, on the top of x^{2}.

And multiply (x - 2) and x.

(x - 2)x = x^{2} - 2x

Write this under x^{2} + 3x.

Subtract (x^{2} + 3x) and (x^{2} - 2x).

x^{2} are cancelled.

+3x - (-2x) = +5x

Bring down the next term -10.

Write it behind 5x.

The goal is to remove 5x of (5x - 10)

by using the divisor (x - 2).

You can make 5x by multiplying (x - 2) and 5.

So write +5 in the quotient, on the top of +3x.

And multiply (x - 2) and +5.

(x - 2)(+5) = 5x - 10

Write this under 5x - 10.

Subtract (5x - 10) and (5x - 10).

Then you get 0.

The remainder is 0.

And the quotient is (x + 5).

So (x^{2} + 3x - 10)/(x - 2) = x + 5.

This is the answer.