00:01
Hello, so here we're going to find all zeros of the function, f of x, which is equal to 3x cubed minus 5x squared minus 18x plus 30.
00:11
So what we can do, we can factor this and factor it by grouping.
00:15
So looking at just the first two terms, 3x cubed and minus 5x squared, where we can pull out an x squared out of those terms, and then we say, well, times what gets us back to the first term, or x squared times 3x is 3x cubed, and x squared times negative 5 is negative.
00:30
Negative 5x square.
00:31
So we have x squared times the quantity 3x minus 5.
00:35
And then looking at the next two terms, negative 18x and 30, we can pull out a negative 6 out of those two terms and then say, well, negative 6 times 3x is negative 18x and negative 6 times negative 5 is 30.
00:47
But now we have two terms and we have a common factor in those terms of 3x minus 5.
00:53
So if we yank out the 3x minus 5 now in front of everything, we factor out the 3x minus 5 and then.
01:00
Then say, well, 3x minus 5 times x squared gets us back to that first term, and then i guess x squared, and then 3x minus 5 times negative 6 is going to be the next term.
01:12
This is going to still be equal to 0.
01:15
So now we have two factors being multiplied equal to 0...