Of negative eight x, negative eight x dividedīy four is negative two, so I'm going to have negative two x. Out of four x squared, I'm just going to be So I could re-write this as four times, now what would it be, four times what? Well if I factor a four

They're not all divisible by x, so I can't throw an x in there. So let's see, they'reĪll divisible by two, so two would be a common factor, but let's see, they'reĪlso all divisible by four, four is divisible by four,Įight is divisible by four, 12 is divisible by four, and that looks like the Try to find the greatest of the common factor, possible common factors There any common factor to all the terms, and I So the way that I like to think about it, I first try to see is So factor this completely, pause the video and have a go at that. In total we have 3 or 1 positive zeros or 2 or 0 negative zeros.See if we can try to factor the following expression completely. Here we can see that we have two changes of signs, hence we have two negative zeros or less but a even number of zeros. In order to find the number of negative zeros we find f(-x) and count the number of changes in sign for the coefficients: Hence our number of positive zeros must then be either 3, or 1. Descartes' rule of signs tells us that the we then have exactly 3 real positive zeros or less but an odd number of zeros. Our variables goes from positive(1) to positive(4) to negative(-3) to positive(1) to negative(-6).īetween the first two coefficients there are no change in signs but between our second and third we have our first change, then between our third and fourth we have our second change and between our 4 th and 5 th coefficients we have a third change of coefficients.

Here are the coefficients of our variable in f(x):

Second we count the number of changes in sign for the coefficients of f(x). Our function is arranged in descending powers of the variable, if it was not in this order we would have to rearrange the terms as our first step. We will show how it works with an example.ĭetermine the number of positive and negative real zeros for the given function (this example is also shown in our video lesson): The number of negative real zeros of the f(x) is the same as the number of changes in sign of the coefficients of the terms of f(-x) or less than this by an even number. It tells us that the number of positive real zeros in a polynomial function f(x) is the same or less than by an even numbers as the number of changes in the sign of the coefficients. Descartes' rule of sign is used to determine the number of real zeros of a polynomial function.

Factoring khan academy algebra 2