Synthetic Division...1

Discussion in 'Algebra' started by nycmathguy, Apr 17, 2022.

1. nycmathguy

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College Algebra
Section R.6

nycmathguy, Apr 17, 2022
2. MathLover1

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correct

MathLover1, Apr 17, 2022
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3. nycmathguy

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I like synthetic division.

Question:

Why does synthetic division only work when dividing by (x - a) or (x + a), where "a" is any integer?

nycmathguy, Apr 18, 2022
4. MathLover1

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Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor -- and it only works in this case.
You can only use synthetic division when you are dividing by something in the form of x±n.
If you are given, say, the polynomial equation y = x^2 + 5x + 6, you can factor the polynomial as y = (x + 3)(x + 2). Then you can find the zeroes of y by setting each factor equal to zero and solving. You will find that x = –2 and x = –3 are the two zeroes of y.

You can, however, also work backwards from the zeroes to find the originating polynomial. For instance, if you are given that x = –2 and x = –3 are the zeroes of a quadratic, then you know that x + 2 = 0, so x + 2 is a factor, and x + 3 = 0, so x + 3 is a factor. Therefore, you know that the quadratic must be of the form y = a(x + 3)(x + 2)

MathLover1, Apr 18, 2022
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5. nycmathguy

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Thanks for the information. Asyou know, we are currently in the review section of the textbook. We haven't done college algebra. I need to practice finding a polynomial function given the zeroes. I think there is a chapter somewhere down the line in this respect.

nycmathguy, Apr 18, 2022

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