00:01
Okay, so for this question we are dividing two polynomials.
00:03
We have 4x to the fifth minus 3x squared plus x plus 1, and we're dividing that by 2x cubed minus 1.
00:12
So first thing we can do is look at our leading terms, and we want to ask ourselves, how many times does 2x cubed go into 4x to the 5th? and we can do that just by doing a division of these two monomials.
00:23
So 4x to the 5th divided by 2x cubed is going to give us 2x squared.
00:29
So this is going to be our.
00:31
First term in our answer so we can go ahead fill that in right over here 2x squared okay and then we have to go back and we need to multiply 2x squared by our divisor 2x cubed minus 1 okay so let's do that now and we can just use the distributive property to do this so we'll get 4x to the 5th minus 2x squared okay, and so we're going to go fill this in right over here.
01:12
So we have 4x to the 5th minus 2x squared.
01:24
Okay, and then just like normal division we can subtract these values.
01:28
So we have 4x to the 5th minus 4x to the 5th that'll give a 0.
01:31
Then we have negative 3x squared minus negative 2x squared which is just going to give us negative x squared remember, subtracting by a negative is just addition.
01:42
And then we want to bring down these last two terms we have over here.
01:45
So we have the plus x and plus one.
01:50
Now if you look at our leading term here, we have negative x squared.
01:54
That is a term of degree two.
01:56
But the leading term of our divisor is actually 2x cubed.
02:00
That's a term of degree three.
02:01
So that means that we can't really do any more division.
02:04
And this polynomial down here is going to be our remainder.
02:07
Okay? so we actually finish the division...