Polynomial long division might feel a little complicated at first, but think of it like solving a puzzle. Here’s an easy guide to help you through it:
Start by writing down the two polynomials.
The first one is called the dividend (the number you want to divide), and the second one is the divisor (the number you're dividing by).
Make sure to line them up from largest to smallest degree.
For example, if you are dividing (2x^3 + 3x^2 - x + 5) by (x + 2), it should look like this:
_______________
x + 2 | 2x^3 + 3x^2 - x + 5
Look at the first term of the dividend and the first term of the divisor.
Divide the leading term of the dividend by the leading term of the divisor.
In this case, divide (2x^3) by (x) to get (2x^2).
Write this number above the division line:
2x^2
_______________
x + 2 | 2x^3 + 3x^2 - x + 5
Now, take the divisor (x + 2) and multiply it by the (2x^2) you just found.
This gives you (2x^3 + 4x^2).
Write this under the dividend, making sure to line up the similar terms.
Subtract it from the original dividend:
2x^2
_______________
x + 2 | 2x^3 + 3x^2 - x + 5
-(2x^3 + 4x^2)
__________________
-x^2 - x + 5
Next, bring down the next term from the original polynomial, which in our case is (-x).
Now, you have (-x^2 - x + 5).
Keep repeating these steps.
Divide (-x^2) by (x) to get (-x).
Write that above the bar, multiply down again, and subtract.
Keep going through these steps: dividing, multiplying, subtracting, and bringing down the next term until you can’t bring down any more terms or your degree is lower than the divisor.
When you're done, the result above the bar is your quotient, and anything left over (if there is any) is your remainder.
For example, if you have a leftover constant like (3), you would write your final answer like this:
And that’s all there is to it!
With practice, this will become easier for you. Don’t worry; the more you try, the more natural it will feel!
Polynomial long division might feel a little complicated at first, but think of it like solving a puzzle. Here’s an easy guide to help you through it:
Start by writing down the two polynomials.
The first one is called the dividend (the number you want to divide), and the second one is the divisor (the number you're dividing by).
Make sure to line them up from largest to smallest degree.
For example, if you are dividing (2x^3 + 3x^2 - x + 5) by (x + 2), it should look like this:
_______________
x + 2 | 2x^3 + 3x^2 - x + 5
Look at the first term of the dividend and the first term of the divisor.
Divide the leading term of the dividend by the leading term of the divisor.
In this case, divide (2x^3) by (x) to get (2x^2).
Write this number above the division line:
2x^2
_______________
x + 2 | 2x^3 + 3x^2 - x + 5
Now, take the divisor (x + 2) and multiply it by the (2x^2) you just found.
This gives you (2x^3 + 4x^2).
Write this under the dividend, making sure to line up the similar terms.
Subtract it from the original dividend:
2x^2
_______________
x + 2 | 2x^3 + 3x^2 - x + 5
-(2x^3 + 4x^2)
__________________
-x^2 - x + 5
Next, bring down the next term from the original polynomial, which in our case is (-x).
Now, you have (-x^2 - x + 5).
Keep repeating these steps.
Divide (-x^2) by (x) to get (-x).
Write that above the bar, multiply down again, and subtract.
Keep going through these steps: dividing, multiplying, subtracting, and bringing down the next term until you can’t bring down any more terms or your degree is lower than the divisor.
When you're done, the result above the bar is your quotient, and anything left over (if there is any) is your remainder.
For example, if you have a leftover constant like (3), you would write your final answer like this:
And that’s all there is to it!
With practice, this will become easier for you. Don’t worry; the more you try, the more natural it will feel!