If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:3:19

Video transcript

we're told we want to find the zeros of this polynomial and they give us the polynomial right over here and it's in factored form and they say plot all the zeros for the x-intercepts of the polynomial in the interactive graph and so this is a screenshot from Kahn Academy if you're doing it on Khan Academy you would click where the zeros are to plot the zeroes but I'm just going to draw it in so pause this video and see if you could have a go at this before we work on this together all right now let's work on this together so the zeroes are the x-values that make our polynomial equal to zero so another way to think about it is for what X values are P of X equal to zero those would be the zeros so essentially we have to say hey what X values would make two x times 2x plus 3 times X minus 2 because this is P of X what X values would make this equal to zero well as we've talked about in previous videos if you take the product of things and that equals zero if any one of those things equal zero at least one of those things equal to zero to make the whole product equal to zero so for example if 2x is equal to zero it would make the whole thing zero so 2 X could be equal to zero and if 2x is equal to zero that means X is equal to zero and you could try that out if X is equal to the zero this part right over here is going to be equal to zero it doesn't matter what these other two things are zero times something something is going to be equal to zero and then you could say well well maybe 2x plus 3 is equal to zero so we could just write that 2x plus 3 is equal to zero and if that were to Drew what would X or what would X have to be in order to make that true subtract 3 from both sides 2x would have to be equal to negative 3 or X would be equal to negative 3 halves so this is another x value that would make the whole thing zero because if X is equal to negative 3 halves then 2x plus 3 is equal to zero you take zero times whatever this is and whatever that is you're going to get zero and then last but not least X minus two could be equal to zero that would make the whole product equal to zero so what x value makes X minus 2 equals zero well add two to both sides and you would get X is equal to two if x equals two that equals zero doesn't matter what these other two things are zero times something times something is going to be equal to zero so just like that we have the zeros of our polynomial and the reason why they have x-intercepts in parenthesis here is that's where the graph of P of X if you say y equals P of X that's where I would intersect the x axis and that's because that's where our polynomial is equal to zero so let's see we have x equals zero which is right over there once again if you were doing this on Khan Academy you would just click right over there and it would put a little dot there we have X is equal to negative three halves which is the same thing as negative one and a half so that's right over there and then we have x equals two which is right over there so those are the x-intercepts or the zeros of that polynomial now this is useful in life because you could use it to graph a function I don't know exactly what this function looks like maybe it looks something like this maybe it looks something like this we would have to try out a few other values to get a sense of that but we at least know where it's intersecting the x-axis it's at the zeros