*dividend*, (2) when the leading co-efficient of the

*dividend*is not 1, (3) when there is a

*remainder*.

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**Situation #1:**How to set up the problem when there is a "missing term" in the

*dividend*.

Look at the problem above. Do you see the where the "missing term" should be? If you look at the exponents of the

*dividend*, you'll see that there is no term for x^2. In order to properly divide these polynomials, we need to

**reintroduce**

*the missing term. We can do that*

__without changing the value of the__

*dividend*by using a co-efficient of zero, as shown circled in red below.

Now that the problem is set up in a familiar way, you can solve it as we did the problem in the Part 1. The steps are shown in the image above.

You should be aware that there may be

__multiple__"missing terms", as in the polynomial (x^5 - x^2 + x). In such a case, introduce enough terms that all exponents are covered. In this example, you would write (x^5

**+ 0x^4 + 0x^3**- x^2 + x

**+ 0**) under the division bar.

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**Situation #2:**The

*dividend's*leading co-efficient is not 1.

The

*leading co-efficient*in a polynomial is the co-efficient on the term with the

__highest exponent__. In the polynomial (2x^3 - x^2 - 3x + 2), the

*leading co-efficient*is 2 because it is on the term with the highest exponent, 3. All of the problems we have dealt with so far have had a

*leading co-efficient*of one. Let's use the polynomial I've given you already to work another division problem.

The first step of this problem is just like the others we have solved. Begin by dividing the first term of the

*dividend*(green circle) by the first term of the

*divisor*(orange box) to get the first term of the

*quotient*(red box). Then, multiply this first term of the

*quotient*by the whole

*divisor*(underlined in purple). This new polynomial (underlined in blue) is written below the

*dividend*and subtracted. Do you see how this step is just like the first step of the other problems we solved? The only, very minor difference, is the initial division of the first terms of the

*dividend*and

*divisor*.

Now, you can finish solving the problem as you would any other, shown below.

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**Situation #3:**The

*remainder*is not zero.

Consider the problem I have worked below. You will notice that at the end, I am left with (-5x+1) (red box). I cannot divide (-5x) by the first term of the

*divisor*, (x^2) because (x^2) is larger. What do we do with this*remainder*?
Your instructor should explain how to represent this remainder. Two representations are given below, although the second looks more professional and is my preference.

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I hope this series has been helpful to you. If you have any questions about this topic or something you would like me to cover in the future, leave them below. Thanks!