12 of 264 Items .... Source: T.R.Milne

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You are asked to find the roots and factors of the following polynomial function:

\( f(x) = x^4 - 2x^3 - 18x^2 + 6x + 45 \)

By the rational root theorem, possible rational roots are
\( \pm ( 1, 3, 5, 9, 15, 45 ) \).

In order to minimize your effort, you know that you should begin with the possibility that is most likely to be a root. Which roots are most likely?

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In a set of data, can the outlier also be the mode or does a number stop being an outlier if it occurs often enough to be a mode?

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Read this post on lost learning time.



Here's his basic point:

... roughly 10 of 60 minutes are not spent learning.
In one day, roughly 50 minutes.
In a 5 day week, 250 minutes.
In a typical school year, 8,700 minutes not utilized for learning.

Now, let's be realistic and cut that number in half because we all know there are assemblies and other events that cut into learning time throughout the school year. That leaves us with 4,350 minutes of time not spent learning.

1. Do you agree with his analysis?


2. How about his calculations?


3. What should be done?

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How many different solutions can we find?

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So ... I've seen a couple of YouTube videos that feature songs about the Quadratic Formula. I often see it written like this:

\(x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}
\)

and it occurs to me that I've always written it this way:

\(x = \dfrac{-b}{2a} \pm \dfrac{\sqrt{b^2-4ac}}{2a}\)

Which one is better?

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How is this problem




related to this one from a few days back?



Is any square number times four another square number?

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What insights does a student need to have before this problem is solvable?

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What is the more critical mistake, the more damaging to civilization as we know it?

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Let's use this Rubik's Cube again, shall we? The total surface area of the cube is 54 square units.

• Is it possible to remove a unit cube without changing the surface area?


• How about removing one that increases the area by 2 square units ....


• or maybe one that can be removed that increases area by 4 sq units?

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That's an 18" diameter pizza plate.
It's the same area as that slice.

What's the girl's name?

Oh, you think you have a better question? Well, do you?

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What question do you want to ask?

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Here are my three brackets:




Which of these is most useful in determining how many people are playing?
How jealous are you right now?