00:01
In this problem, we're told that dividing x plus 2 into 2x cubed plus a squared plus 3x minus 4 and into x cubed plus x squared minus 4x plus a yields the same remainder.
00:13
Our job is to answer the question, what is a? we note that if dividing x plus 2 into these two polynomials yields the same remainder, then if we subtract the two polynomials, dividing x plus 2 into that result will yield a zero remainder.
00:28
So we're going to start by subtracting.
00:32
We're going to calculate the difference in those two polynomials.
00:36
So we'll take the first one, and we will subtract the second one to see what the result is.
00:58
So subtracting yields x cubed plus.
01:03
Now the coefficient of x squared becomes a minus 1.
01:11
Then we have 7x, and finally the constant coefficient becomes negative 4 minus a.
01:18
We're going to let that difference be represented by f of x.
01:23
Now here's our claim.
01:25
Our claim is that the remainder when we divide f of x by x plus 2 has to be 0.
01:30
So x plus 2 is a factor of this...
