# Tutor profile: Justin T.

## Questions

### Subject: Pre-Calculus

How would I simplify a polynomial function that is divided by another polynomial function?

This question can be a bit tricky while still learning it, but once you know how to break it down in steps, it is not that bad. A very quick example would be something like this: $$\frac{x^3 + 3x - 2}{x + 3}$$. While this may look scary, it is rather simple as it works just like normal long division. First, you would make sure everything is in descending order. In this case, the equation is in descending order as the exponents over the x in each case gets lower. If it is ever not, just rearrange them making sure to keep the addition and subtraction symbols the same. Next, make sure to check that all of the x's are not missing any exponents in order. For example, this top line is missing an $$x^2$$ after the $$x^3$$. To fix this, just add a $$0x^2$$ to keep track of everything a little easier. Now, comes the real division. To do this, it is as simple as understanding what needs to be done to the divisor to get rid of parts of the numerator. We will focus first on the $$x^3$$ as you must go in order. To get from $$x$$ to $$x^3$$ you would multiply $$x$$ by $$x^2$$. Then, do the same thing for the +3. Our new denominator for this part is now $$x^3 + 3x^2$$. Then, simply multiply this by -1 to get $$-x^3 - 3x^2$$ and subtract. Remember we inserted $$0x^2$$ into this--> $$(x^3 + 0x^2 + 3x - 2) + (-x^3 -3x^2)$$ then equals $$-3x^2 + 3x - 2$$. So, our new equation to continue with division is $$\frac{-3x^2 + 3x - 2}{x+3}$$ and is simply completed by continuing with this same strategy. If there is any remainder at the end, it will be expressed as + $$\frac{remainder}{x+3}$$.

### Subject: Astronomy

Can you explain the light spectrum and how to remember the different parts of it?

The light spectrum is a great topic. It can be a little hard to understand, but it all has to do with the individual particles of light called photons. These photons are the things that go through the pupil in your eye and hit your retina, causing some biological stuff to happen for us to see. What exactly we see is determined by a few characteristics of the light particles. Their wavelength, frequency, and energy. Wavelength is the distance between the peaks as light moves as a wave. Frequency is the number of waves that pass a point in an amount of time, usually a second. The energy of the light is determined by taking the wavelength and dividing it by the frequency. Using this knowledge, we can then learn a bit about how each one interacts with where light is on the spectrum, and what color the light is if it is visible light. The light spectrum is divided up into how much energy the light photons have. The very bottom of the spectrum is radio waves. These have the least amount of energy, the greatest wavelength, and the highest frequency. Next is microwave, followed by infrared, then the visible light we see, ultra-violet, x-ray, and lastly gamma rays. With each successive jump in energy, so too does the frequency increase. Even in the visible spectrum, as light has more energy it has more frequency and shifts more toward the blue end of the spectrum. Inversely, as the energy and frequency of light increases, the wavelength of light decreases. Frequency/Energy and wavelength are inversely proportional, meaning as one increases, the other will decrease. This should make it a little less confusing when coming upon these topics in the future.

### Subject: Physics

What is the difference between speed, velocity, and acceleration?

While all clearly related, speed, velocity, and acceleration are calculated differently and are used for different applications. Speed is, simply put, the time it takes to move a certain distance. This is calculated as distance traveled divided by time it took to move that distance $$(d/t)$$. Speed will always be positive if it is not zero. Ex: If a bus travels 100 km in two hours, we take the distance (100km) and divide by the time (2hr) to calculate the speed of 50 $$km/hr$$. Velocity is very similar to speed, but what is called a vector. This means that it has a direction such as 5 km/hr north, or due north, etc. This is calculated similarly, but using displacement instead of distance. This can be either positive or negative depending on the displacement, or zero if the displacement is zero. Acceleration is also similar to speed, but it is the change in velocity over time. This is calculated similarly by taking the velocity and dividing it by the time again, usually in meters and seconds $$(m/s^2)$$. This can be positive if speeding up, negative if slowing down, or zero if going a constant speed.

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