00:01
So if we have 3 minus 5i is a root, then also a 0, then 3 plus 5i must also be a root.
00:11
And the way i like to do a problem like this, some different teachers teach it differently, is that its factors need to be the opposite of that.
00:21
X minus.
00:23
So what you can do is you can multiply this out.
00:27
Next times x is x squared.
00:29
The outside you also have to distribute that negative in there so we're looking at negative 3x and then a negative 5x i but then you have to distribute the x in here and again distribute that negative so it's another negative 3x but this is a plus 5xi and i like to just multiply the last one because the negative times the negative is positive 3 times 3 would be 9 you get a 15 i and immediately a negative 15 i some people call this foiling by the way if you've heard that phrase before and negative 5 times 5 is negative 25 and i times i is i squared and the whole point of this is all of these is will eliminate except this i squared but that's equal to negative 1 so it becomes plus 25 so what we're looking at is x squared minus 6x and 9 plus 25 is 34.
01:32
And the whole point of doing all that work then is that should also be a factor of this x to the fourth minus 2x cubed minus 2x squared plus 208x minus 408 and 8 and you do long division that x squared times x squared gives me x to the fourth and then you have to distribute that x squared to everything and remember to subtract off each of those pieces so now we're looking at 4x cubed minus 36 x squared and bring down that 208x and so now x squared times 4x gives me 4x cute but again you have to distribute so minus 24 x and 4 times 34 is 136 but then you have to subtract that off and this time, i end up with, what would that be? nope, negative 36 plus 24 is negative 12.
02:56
I did the wrong way.
02:59
X squared and 208 minus 136 is 72.
03:08
Bring that 408 down.
03:11
And then same question...