This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

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A **polynomial **is a mathematical expression consisting of exponents, constants and variables.

Example:

The **degree of the polynomial** is the value of the highest exponent. For instance, in the above example, 3 is the highest exponent, so the degree of the polynomial is 3.

In a polynomial, the __exponents need to be non-negative integers__ : 0, 1, 2, 3, … and we __cannot__ divide by variables.

** Examples that are not polynomials**:

\(x^{-2} + x\) (we cannot have a negative exponent)

\(\frac{x}{x + 2}\) (We cannot have division by a variable)

\(x^ {\frac{1}{2}}\)^{ } (The exponent cannot be a fraction)

We can divide one polynomial by another polynomial using long division. Polynomial long division is similar to long division of numbers.

When we divide, the polynomials’ terms __should be arranged in decreasing order of exponents__, from the highest exponent to the lowest exponent.

For example, if we have \(x^2 + x^4 + 1\), it should be rearranged as \(x^4 + x^2 + 1\).

Suppose the question is \(\frac{x^4 + x^2 + 1}{x+2}\), then \(x^4 + x^2 + 1\), the **numerator**, is called the **dividend** (the number that is going to be divided) and \(x + 2\), the **denominator**, is called the **divisor** (the number that we are dividing by).

Please note that the following notations are __equivalent__:

There are 3 steps to doing polynomial long division:

**Divide**: Divide the first term of the dividend (numerator) by the first term of the divisor (denominator).**Multiply**: Multiply the answer from step 1 with the divisor and write it below the dividend.**Subtract**

and **repeat **the process.

Let us see an example!

In the above video, we didn’t have a remainder - remainder was 0. But that’s not always the case. The next video shows an example where we have a non zero remainder at the end.

Sometimes, we have missing terms that is we don’t have all the exponents in the dividend (numerator).

For example in the question, \((x^4 + x^2 + 1) \div (x+2) \), in the dividend (numerator), we are missing terms with exponent 3 and exponent 1. The next video shows an example where we have missing terms in the dividend (numerator).

Now let's practice!

- Last Updated: Aug 1, 2024 10:46 AM
- URL: https://libraryguides.centennialcollege.ca/mathhelp
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