00:01
This problem gives us the function f of x equals x q minus 7x squared plus 13x minus 7 and it wants us to find the zeros, even the irrational zeros, and the factored form after we figure out what the zeros are.
00:12
So factoring by grouping won't work for this one, so we would be stuck with doing the possible rational zeros where we put the factors of the last value 7.
00:21
In other words, p over the factors of the constant or the coefficient of the first term q.
00:26
So we have 1 and 7 from 7 and understood 1 from the 1x cube.
00:32
So a pretty small list.
00:34
And remember it is the positive and negative versions of this.
00:36
So we have positive negative 1 and positive and negative 7.
00:40
So we would kind of basically just kind of testing guess to see which one of these could break down our function.
00:45
And we'll start with 1.
00:48
And to do synthetic division, we'll take the coefficients of the original function.
00:52
So 1x cubed minus 7x squared plus 13x.
00:56
Minus seven.
00:58
So we'll bring down the first number to begin to the egg division.
01:00
One times one is one.
01:02
Negative seven plus one is negative six.
01:04
Negative six now times the one on the outside is negative six...