00:01
So if we write out p of x here, we've got a cubic.
00:04
Now, we know with quadratic how to solve them, but with cubic, we can't really do that by inspection.
00:10
So we need to use a few tricks, namely two theorems, the rational root theorem and factor theorem.
00:25
Now, the rational root theorem states that any rational root written in lowest terms has a numerator that is a factor of the constant term 16, and a denominator that is a factor of the leading coefficient 2.
00:38
So the possible factors we have that we would expect from the rational root theorem, plus or minus 1, plus and minus 4, plus or minus 8, and plus or minus 60.
00:51
So testing a few of these, we actually find out that x, oh sorry, we find out that x equal to 4 solves this equation...