00:01
This problem wants us to find the zeros of the following polynomial amount to three decimal places when necessary.
00:05
And we're given a four -term polynomial in standard form, and this can't be factored by grouping.
00:10
So our next step would be to, at least to do this by hand, would be to find the factors of our p value, which is our constant, and put them over the factors of our q value, which would be the leading coefficient.
00:21
So that would be just 1 and 41, because 41's a prior number over the understood 1.
00:27
So there's not a lot of choices, and that would be the positive and negative of each version.
00:31
So when we look at our possibilities and we test them, the first one that tests and gives us a zero using synthetic division would be negative 1.
00:40
And to do synthetic division to show that, but to also start to break down our functions so we can find the other zeros, we would have negative 1 on the outside of our synthetic division with 1x cubed for a coefficient, and then 11x squared, 51x, and 41.
00:54
And to begin, synthetic division, we'll bring down the first number, and then we'll multiply by our value on that.
00:58
Outside, which is negative 1, and we'll write the result underneath our next number.
01:02
So 1 times negative 1 is negative 1.
01:04
Now we'll add straight down vertically.
01:06
11 plus negative 1 is 10.
01:08
10 now times our number on the outside again, negative 1 gives us negative 10...