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 (x2 + 3x - 10) in the form.
And write the divisor (x - 2) in the left side of the form.

The goal is to remove x2 of (x2 + 3x - 10)
by using the divisor (x - 2).

You can make x2 by multiplying (x - 2) and x.

So write x in the quotient, on the top of x2.
And multiply (x - 2) and x.
(x - 2)x = x2 - 2x
Write this under x2 + 3x.

Subtract (x2 + 3x) and (x2 - 2x).
x2 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 (x2 + 3x - 10)/(x - 2) = x + 5.
This is the answer.