- 1). Find the polynomial constant. Every polynomial has, as its last term, a constant. The last term is just a number, not multiplied by any variable. Any factors of the whole polynomial will involve numbers that can evenly divide into the polynomial constant. If the polynomial has a variable, like x, as its last factor then the polynomial constant is taken to be zero.
- 2). Find the numbers that divide into the last term evenly. For instance, if the last term is 20 then the numbers that divide into it evenly are 1, 2, 4, 5, 10, 20, -1, -2, -4, -5, -10 and -20. One or more of these numbers will be a part of the polynomial's factors.
- 3). Try these numbers, one after the other, in the equation. Everywhere there is a variable, plug in the numbers. For instance, if you are factoring the polynomial 2x-20, first substitute the number one for x and do the sum. Then do it again with a 2 in place of the x, and then a 4, and so on. If the result is zero, record that number. It is part of one of the factors in the polynomial.
- 4). Subtract any number that makes the polynomial equal to 0 from the polynomial's variable. For instance, in the above example of 2x-20, because substituting 10 for x makes the polynomial zero, then (x-10) is a factor of the polynomial.
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