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Current time:0:00Total duration:3:32

Video transcript

so we're given a P of X it's a third degree polynomial and they say plot all the zeros or the x-intercepts of the polynomial in the interactive graph and there is why they say interactive graph this is a screenshot from the exercise on Khan Academy where you could click and place the zeroes but the key here is let's figure out what X values make P of X equal to zero those are the zeros and then we can plot them so pause this video and see if you can figure that out so the key here is to try to factor this expression right over here this third degree expression because really we're trying to solve the X's for which five X to the third plus five x squared minus 30x is equal to zero and the way we do that is by factoring this left hand expression so the first thing I always look for is a common factor across all of the terms it looks like all the terms are divisible by five X so let's factor out a 5 X so this is going to be 5x times if we take a 5 X out of 5 X to the third we're left with an x squared we take out a 5 X out of 5 x squared we're left with an X so plus X and if we take out a 5x of negative 30x we're left with a negative 6 is equal to zero and now we have 5x times this second-degree the second-degree expression and to factor that let's see what two numbers add up to one you could view this as a One X here and their product is equal to negative six and let's see positive 3 and negative 2 would do the trick so I can rewrite this as 5x times so X plus 3 X plus 3 times X minus 2 and if what I just did looks unfamiliar I encourage you to review factoring quadratics on Khan Academy and that is all going to be equal to zero and so if I try to figure out what X values are going to make this whole expression zero it could be the x values or the x value that makes 5x equals zero because if 5x is zero zero times anything else is going to be zero so what makes five X equal zero well if we divide 5 if you divide both sides by five you're going to get X is equal to zero and it is the case if x equals zero this becomes zero and then doesn't matter what these are zero times anything is zero the other possible x-value that would make everything zero is the x value that makes x plus three equal to zero subtract three from both sides you get X is equal to negative three and then the other x value is the x value that makes X minus two equal to zero add two to both sides that's going to be x equals two so there you have it we have identified the three X values that make our polynomial equal to zero and those are going to be the zeros and the x-intercepts so we have one at x equals zero we have one at x equals negative three we have one at x equals at x equals two and the reason why it's we're done now with this exercise if you're doing some kind of kind of you were just clicked into these three places but the reason why folks find this to be useful is it helps us start to think about what the graph could be because the graph has to intersect the x-axis at these points so the graph might look something like that it might look something like that and to figure out what it actually does look like we'd probably want to try out a few more x-values in between these x-intercepts to get the general sense of the graph