## Possible Factors of Polynomials

When looking at possible factors of a polynomial it is necessary to look at the coefficients of the highest and lowest powers of If a factor of the polynomial is then must be a factor of the coefficient of the highest power of and must be a factor of the lowest power of For example if then possible factors are We can however cut down the number of possible options by looking at the coefficients. The negative coefficient of and the positive coefficient of and the positive constant (the coefficient of ) dictate factors of the form Only the last four factors are possible therefore.

Now we can instead use the fact that if is a factor then is a root so If is a factor then If is a factor then If is a factor then If is a factor then We can try each of these in turn though of course it being easing to work with integers, first find and  so is not a factor. so is a factor. so is a factor.

Since is a quadratic it only has two factors and If p(x) is a quadratic or polynomial of higher degree, this method is probably the best method that can be used with pencil and paper. Suppose that Possible factors are Running though the possible roots gives eventually that so and is a factor. Long division of by gives the quadratic which can be easily factorised as then 