Yeah, you can actually see with the naked eye, without all this rigmarole. a^2 is common on the lh side at the start, so factor it out. You get a^2 (a - 1). You can immediately see that a = 3 satisfies this equation, since a^2 = 9 and a - 1 = 2. 2 x 9 =18. Done.
Silly problem…. Right from the start you begin with 27-9 because obviously you’re looking for numbers that can be cubed and squared then subtracted and obviously 3^3-3^2=18 so we’re done because any moron can see that a = 3 by pattern. Done . Not sure of the point of this vid. Even to find your other solutions, just use synthetic division with the 3 that you find to reduce it to a quadratic equation which you could then solve for the other two solutions.
At 1:06 you diverged from teaching them anything. You wrote 27-9 because you had rigged the problem to come out that way. You then dragged them through a bunch of rewriting that you could do only because you knew how the problem was going to end. Instead, you should have shown them the Rational Root Theorem and found a=3 as a root of the cubic. Then you should have shown them polynomial division and found a^2 + 2a + 6 as the other factor. Then you should have shown them how to complete the square and find a = -1+-sqrt(5) as the other two roots. What a pointless video.
By inspection : a²*(a-1)=18=3²*2
a=3
Soooooo...you already have to know the answer to get the answer...got it.
Yeah, you can actually see with the naked eye, without all this rigmarole. a^2 is common on the lh side at the start, so factor it out. You get a^2 (a - 1). You can immediately see that a = 3 satisfies this equation, since a^2 = 9 and a - 1 = 2. 2 x 9 =18. Done.
Silly problem…. Right from the start you begin with 27-9 because obviously you’re looking for numbers that can be cubed and squared then subtracted and obviously 3^3-3^2=18 so we’re done because any moron can see that a = 3 by pattern. Done . Not sure of the point of this vid. Even to find your other solutions, just use synthetic division with the 3 that you find to reduce it to a quadratic equation which you could then solve for the other two solutions.
But you did not solve the problem.
The problem was to "solve for x." 😀
At 1:06 you diverged from teaching them anything. You wrote 27-9 because you had rigged the problem to come out that way. You then dragged them through a bunch of rewriting that you could do only because you knew how the problem was going to end. Instead, you should have shown them the Rational Root Theorem and found a=3 as a root of the cubic. Then you should have shown them polynomial division and found a^2 + 2a + 6 as the other factor. Then you should have shown them how to complete the square and find a = -1+-sqrt(5) as the other two roots. What a pointless video.