Dividing Polynomials

Divide the following:

5x³ - 29x² + 55x - 28
            5x - 4

Change it to the following:

Now just look at the beginning terms and ask, how many times does 5x go into 5x³? The answer, of course, is x² times since 5x(x²) = 5x³. So we begin the quotient with x² and multiply it by the divsor (5x-4) and place the result under the dividend and substract and bring down the remainder of the dividend (in red):

Now, cycle through again, looking at the first terms. How many times does 5x go into -25x²? -5x is the answer. So, put that as part of the quotient and multiply -5x and (5x + 4) and put the value below, subtract, and bring down the remainder (in red):

Now, cycle through again, looking at the first terms. How many times does 5x go into 35x? The answer is 7. So, put that as part of the quotient and multiply 7 and (5x _ 4) and put the value below, subtract:

So the answer is x² - 5x + 7.

Now this one ends up being nice to us since it ends in 0. Say, we ended up with a 1 instead. Then we would divide by the 1 by the divisor (5x - 4) and add that fraction to the quotient.

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