I have a 7th degree polynomial. What is the first step to use to start to get the factors for this polynomial?
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If there are only positive coefficients, the zeroes (from which factors can be deduced) will all be negative.
For mixed positive and negative coefficients, usually there are some simple zeroes like 1 and -1 that can be substituted for the variable that give a zero result.
The size of the coefficients are also likely to be small numbers.
Look out for missing powers; that may be an indication that the polynomial has a factor involving x^2 rather than x, for example.
When you find a factor divide the polynomial by it using algebraic or synthetic division. This will reduce the degree.
The method I find to be most effective is to use my calculator to plug in trial values for the variable between, say, -5 and +5 in steps of 1. When the result changes sign between two consecutive integers, I know there's a zero between; and occasionally an integer will itself produce zero, so I know that integer is a zero.
Once a zero is located between two integers I can then home in on values in between. In a 7-degree poly you may have up to 7 factors so you do have to keep looking. Once you have found 5 factors using zeroes (if a is a zero then x-a is a factor), you will be left with a quadratic which may or may not factorise further, but you can apply the formula in any case.

I hope this helps.
by Top Rated User (1.1m points)

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