00:01
We're going to take a look at three different problems here.
00:03
The first of which is using synthetic division and the remainder theorem to find the indicated function value, which is f of 3 on the polynomial f of x equals x to the third minus 7x squared plus 5x minus 6.
00:18
So the remainder theorem states that when we divide a function like f of x by, say, a factor x minus 3 in this case, then the remainder would give us whatever f of 3 is.
00:32
So we're not actually evaluating here.
00:34
We're going to use synthetic division in the idea that we are dividing by x minus 3.
00:41
So to do so, i would use coefficients of all of these.
00:48
1, negative 7, positive 5, and negative 6.
00:53
Drop the 1, 3 times 1 is 3.
00:55
Add them, we get negative 4, multiply.
00:57
We get negative 12.
00:59
Add them negative 7, multiply negative 21, add them negative 27.
01:10
What that tells us is that our remainder, given the remainder theorem, would be negative 27.
01:16
So given the options over here for multiple choice, choice a makes the most sense.
01:23
The second problem, we want to find the y intercept of f of x equals negative 2 times x minus 4 squared times x squared minus 25.
01:32
Right now this is in factored form, so we could expand it in order to see that y intercept.
01:39
That y intercept would be whatever the constant is.
01:42
And we don't necessarily have to multiply it all out to do that.
01:47
So we'll take a look at what we can see here.
01:51
So first is to recognize when we expand x minus 4 squared, we get x squared minus 8x plus 16.
02:04
And then from there, like i said, we don't need to extend this out much first.
02:07
We just need to recognize that this negative 2 is going to multiply by the 16 to get us our last term once multiplied by that negative 25.
02:18
So that means we're going to have a negative 2 times positive 16 times a negative 25.
02:25
So negative 32 times negative 25, which is a positive 800...