00:01
So here we are to find all of the zeros for the polynomial function, 8x of the 5th, minus 14x of the 4th, minus 22x of the 3rd, plus 57x squared, minus 35x plus 6.
00:19
And so, first thing we know from this, the possible rational roots would be the factors of 6 over the factors of 8, and the factors of six are one, two, three, and six, and the factors of eight are one, two, four, eight.
00:43
And so that makes plus and minus one, two, three.
00:47
Six are possible roots.
00:50
One half, three halves.
00:55
Six halves are the same as three, so we don't need that one.
00:58
Then you'd have one -fourth.
01:02
Two -fourths is like one -half, three -fourths.
01:07
And six -fourths.
01:08
Is like 3 over 2.
01:11
And then you'd have 1 eighth, 2 8ths is 1 4th, 3 8s, and then 6 .8s is like 3 .4s.
01:21
So these are the numbers that you possibly could use for our synthetic division.
01:29
And so 8, negative 14, negative 22, 57, negative 35, and 6.
01:40
And so the first number we are going to try.
01:43
Would be a positive one.
01:49
So if we put a one there, we get 8, 8, negative 6, negative 6, negative 28, negative 28, 29, 29, negative 6, 0, so 1 is a possible, or 1 is an actual root.
02:15
Now we're left with 8x to the 4th, minus 6x to the 3rd, minus 28x plus 29, minus 28x squared plus 29x minus 6.
02:30
Still have 6 and 8 as our leading coefficient constant.
02:34
And so the next number we're going to try is a negative 2.
02:41
So if we put a negative 2 here, that would be 8, negative 16, negative 22, 44...