polynomial division

Polynomial Division

Algebraic division is when you have two algebraic expressions, like numbers with letters mixed in, and you want to divide them just like you would divide regular numbers.

Basic Example

Let’s say we have the problem: (2x^2 + 4x) / (2x). This means we want to divide the expression 2x^2 + 4x by 2x.

The Solution

To solve this, we can use long division, just like with regular numbers.

• First, we divide the first term of the numerator by the denominator. So 2x^2 divided by 2x is x. We write x above the line.
• Next, we multiply the x we just found by the denominator (2x) and write the result (2x^2) below the first term of the numerator.
• Then we subtract (2x^2 + 4x – 2x^2) and we get 4x. Write that below the line.
• Now we bring down the next term of the numerator, which is +0. We divide 4x by 2x and get 2. Write 2 above the line.
• Multiply 2 by the denominator (2x) and write the result (4x) below the next term of the numerator.
• Subtract (4x – 4x) and we get 0. Since we have no more terms to bring down, we are done.

So our final answer is x + 2.

Therefore, (2x^2 + 4x) / (2x) = x + 2.