00:01
All right, so we're trying to find a value for k that makes 4x minus 3 be a factor.
00:08
And i'm going to do a long division, which is how i like to do the problem.
00:13
And if it's a factor, it's just saying that, hey, we're going to get a remainder of zero.
00:19
Plus 23x squared.
00:24
And you could probably do this using, i don't know if that's a plus or a minus 10k.
00:32
I guess i could probably do it both ways.
00:35
Was it 10x? and then plus k it's like a question mark where that plus is but uh i don't even need that for a while so uh again the underlying thing is if this is a factor let me change colors if this is a factor that means that it divides evenly and you get a remainder of zero so it actually doesn't matter that this is a plus or minus for a while so let me just work through it so what times 4x would give me 20x cube that would be 5x squared and then when i multiply 5x squared times 4x, i get 20x cubed.
01:15
And 5 times 4, sorry, 3 is 15.
01:18
I should make a negative x squared.
01:21
And then you have to subtract off each of those pieces.
01:24
That's kind of ugly.
01:27
What's that? 38x squared.
01:30
And this is where it matters when you bring down that 10x or if it's a minus 10x.
01:35
So maybe i'll just work through it both ways.
01:37
I don't know.
01:38
So what times 4 would give me 38? i can use a calculator, i guess.
01:53
Well, 36 would be 9.
01:58
So it's got to be 9 1ā2.
02:00
9 and a half.
02:02
38 divided by 4.
02:05
Yeah, 9 .5.
02:06
If i change that to a fraction, i might make it easier.
02:09
Change to a fraction.
02:10
It would be 19 halves.
02:15
So as i multiply that in, i'll get 38.
02:18
X squared again and 19 halves times negative 3 negative 57 halves and then as i subtract i'll change that to a plus and this is where that plus matters that i can't really read in your problem if it's a plus 10x and you add so 10 plus that value is 77 halves but if it were a minus 10 i had a negative 10 and add that 57 halves.
03:05
I'll get 37 halves...
