00:01
In this problem, we're being asked to find all of the real zeros for the given equation.
00:04
Well, we have our rational zeros theorem, which tells us our list for potential rational zeros.
00:11
To find them, we have to do the factors of our constant divided by the factors of our leading coefficient.
00:15
So in this case, we would have to do the factors of our constant, which is three, divided by our leading coefficient, which is one, so the factors of one.
00:24
Well, the only factors of three are 1 and 3, and the factors of 1 are simply just 1.
00:30
So when we divide, we have 1 divided by 1, which is equal to 1.
00:33
So our first pair of factors would be plus and minus 1, and 3 divided by 1 is 3.
00:38
So our other factors would be plus or minus 3.
00:41
So from here, we just need to substitute these values into our formula to figure out which one's 0.
00:46
Well, what you'll find is when you substitute 3 in place of y.
00:50
Let's make that a 3.
00:53
So 3 squared minus 2 times 3 minus 3 this is in fact equal to 0 which means that y is equal to 3 is one of our zeros for this equation well if y equals 3 is a 0 then y minus 3 is a factor so what we need to do is divide our original equation by y minus 3 to do this i'll use synthetic division so i'll put our 3 inside our half box and then i'll bring down the coefficients for each of our terms so those would be 1 negative 2 negative 2 and negative 3 so then i'll leave a little bit of space, bring down the first one, one...