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Dividing Polynomials: Algebra 2/Trig.

Greeting math peeps! In this post we are going to go over dividing polynomials! At some point, you may need to know how to answer these types of questions. The cool thing about dividing polynomials is that it’s the same long division you did way back in grade school (except now with a lot of x). Ok, let’s get to it and check out the question below:

Also, if you haven’t done so, check out the video related that corresponds to this problem on Youtube below! 🙂

Explanation:

How do I answer this question?

The question wants us to divide polynomials by using long division.

How do we do this?

Step 1: First we set up a good ole’ division problem with the divisor, dividend, and quotient to solve.

Step 2: Now we use long division like we used to back in the day! If you have any confusion about this please check out the video in this post.

What if there’s a Remainder?

What happens when there is a remainder though!?!? When dividing polynomials with a remainder in the quotient, the answer is found and checked in a very similar way! Check it out in the example below:

Notice we represented the remainder by adding to our quotient! We just put the remainder over the divisor to represent this extra bit of solution.

Want more practice? Try solving these next few examples on your own.

Practice Questions:

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Solutions:

If you’re looking for more on dividing polynomials, check out this post on synthetic division and finding zeros here!

Still got questions? No problem! Don’t hesitate to comment with any questions or check out the video above. Happy calculating! 🙂

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Earth Day Fractals!

In honor of Earth Day last week, I thought we’d take a look at some math that appears magically in nature. Math? In nature? For those of you who think math is unnatural or just terrible in general, this is a great time to be proven otherwise!

The key that links math to nature is all about PATTERNS. All math is based on is patterns. This includes all types of math, from sequences to finding x, each mathematical procedure follows some type of pattern. Meanwhile back in the nearest forest, patterns are occurring everywhere in nature.

The rock star of all patterns would have to be FRACTALS. A Fractal is a repeating pattern that is ongoing and has different sizes of the exact same thing! And the amazing thing is that we can actually find fractals in our ~~neighbor’s~~ local garden.

Let’s look at some Fractal Examples:

(1) Romanesco Broccoli: Check out those repeating shapes, that have the same repeating shapes on those shapes and the same repeating shapes on even smaller shapes and…. my brain hurts!

(2) Fern Leaves: The largest part of this fractal is the entire fern leaf itself. The next smaller and identical part is each individual “leaf” along the stem. If you look closely, the pattern continues!

(3) Leaves: If you’ve ever gotten up real close to any type of leaf, you may have noticed the forever repeating pattern that gets smaller and smaller. Behold the power and fractal pattern of this mighty leaf below!

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Just in case fractals are still a bit hard to grasp, check out the most famous Fractal below, otherwise known as Sierpinski’s Triangle. This example might not be found in your local back yard, but it’s the best way to see what a fractal truly is up close and infinite and stuff.

Looking for more math in nature? Check out this post on the Golden Ratio and happy calculating! 🙂

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Perpendicular Lines through a Given Point: Geometry

Ahoy math peeps! I’m writing this during the time of the coronavirus, and although, the NYS Regents tests may be canceled, online zooming is still on! From the good ole’ days of test-taking and sitting in a giant room together, I bring to you a Regent’s classic, a question about how to find perpendicular lines through a given point. We will go over the following Regents question, starting with a review of what perpendicular lines are. Stay curious and happy calculating! 🙂

Perpendicular Lines: When two lines going in opposite directions come together to form a perfect 90º angle! Sounds magical, am I right? Check it out for yourself below:

Perpendicular Lines through a Given Point

A super exciting feature of these so-called perpendicular lines is that their slopes are negative reciprocals of each other. Wait, what?

How do we do this? Now it is time to go back and answer our question!

First, our equation 2y+3x=1 looks kind of cray, so let’s get it back to normal in y=mx+b form:

Need more of an explanation? Check out the video that goes over these types of questions up on Youtube (video at top of post) and let me know if you have still any questions.

Happy Calculating! 🙂

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Looking for more on Perpendicular and parallel lines? Check out the difference between the two in this post here!

COVID-19: What does #FlattenTheCurve even mean?

COVID-19: What does #FlattenTheCurve even mean? If you are a human on Earth, then I’m sure you’ve heard about the coronavirus and are currently social distancing. Here in NYC, I’m quarantining like everyone else and listening to all the beautiful math language that has suddenly become mainstream (so, exciting)! #FlattenTheCurve has become NY’s new catchphrase and for anyone confused about what that means, you’ve come to the right place!

The coronavirus spreads at an Exponential Rate, which means it spreads in a way that increases faster and faster every day.

What does this mean?

For Example, one person with the virus can easily spread the virus to 5 other people, those 5 people can then spread the virus to another 5 people each for a total of an extra 25 people, these 25 people can then spread it to another 5 people each for an extra 125 infected people! And the pattern continues……. See below to get a clearer picture:

COVID-19: What does #FlattenTheCurve even mean?

. *Note: These numbers are not based on actual coronavirus data

The Example we just went over is equal to the exponential equation , but it is only that, an Example! The exact pattern and exponential equation of the future progress of the virus is unknown! We mathematicians, can only measure what has already occurred and prepare/model for the future. To make the virus spread less rapidly, it is our duty to stay home to slow the rate of this exponentially spreading virus as much as possible.

We want to #FlattenTheCurve a.k.a flatten the increasing exponential curve of new coronavirus cases that appear every day! Hopefully, this post brings some clarity to what’s going on in the world right now. Even with mathematics, the true outcome of the virus may be unknown, but understanding why we are all at home in the first place and the positive impact it has is also important (and kind of cool).

Stay safe math friends and happy calculating! 🙂

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Math Resources (in the time of COVID)

Calling all students, teachers, and parents! As everyone is stuck at home during a global pandemic, now is a ~~great~~ time we are all forced to try and understand math (and our sanity level) a little bit more. Well, I may not be able to help you with the keeping sanity stuff, but as far as math goes, hopefully, the below math resources offer some much needed mathematic support.

All jokes aside I hope everyone is staying safe and successfully social distancing. Stay well, math friends! 🙂

Kahn Academy: The same Kahn Academy we know and love still has amazing videos and tutorials as usual, but now they also have a live “homeroom” chat on Facebook LIVE every day at 12:00pm. The chats occur daily with Kahn Academy founder Sal and at times feature famous guests such as Bill Gates. Click the link below for more:

Khan Academy Homeroom

Study.com: In a time when companies are being more generous, Study.com is here for us as they offer up to 1000 licenses for school districts and free lessons for teachers, students, and parents. Check out all the education freebies here:

Study.com

Math Planet: If you’re looking for free math resources in Pre-Algebra, Algebra, Algebra 2, and Geometry then you will find the answers you need at Math Planet. All free all the time, find their website here:

MathPlanet

MathSux: Clearly, I had to mention MathSux, the very site you are on right now! Check out free math videos, lesson, practice questions, and more for understanding math any way that works for you!

MathSux

What is your favorite educational site? Let me know in the comments, and stay well! 🙂

Binomial Cubic Expansion: Algebra 2/Trig.

Hey math friends! In this post, we are going to go over Binomial Cubic Expansion by going step by step! We’ll start by reviewing an old Regents question. Then, to truly master the topic, try the practice problems at the end of this post on your own! And, if you still have questions, don’t hesitate to watch the video or comment below. Thanks for stopping by and happy calculating! 🙂

Also, if you’re looking for more on Binomial Cubic Expansion, check out this post here!

What are Cubed Binomials?

Binomials are two-termed expressions, and now we are cubing them with a triple exponent! See how to tackle these types of problems with the example below:

How do I answer this question?

We need to do an algebraic proof to see if (a+b)³=a³+b³.

How do we do this?

We set each expression equal to one another, and try to get one side to look like the other by using FOIL and distributing. In this case, we will be expanding (a+b)³ to equal (a+b)(a+b)(a+b).

Extra Tip! Notice that we used something called FOIL to combine (a+b)(a+b). But what does that even mean? FOIL is an acronym for multiplying the two terms together. It’s a way to remember to distribute each term to one another. Take a look below:

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Add and combine all like terms together and we get !

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Keep in touch with MathSux and get FREE math videos, lessons, and practice questions straight to your inbox! Thanks for stopping by and happy calculating! 🙂

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Rate of Change: Algebra

The rate of change, the rate of motion, the rate of a heartbeat. A chart on a piece of paper as boring as it may seem, can produce some pretty great numbers that directly relate to us human folk.

The question below may make you groan at first glance, but what happens if we use our imagination to picture the real-life bird it’s describing? Any better? Yes? No? Well, either way we must solve, so let’s get to it

How do I answer this question?

It wants us to find the Rate of Change, specifically between 3 and 9 seconds. Let’s hi-light those two values on our given table:

What is the Rate of Change?

To get the Rate of Change between these two values, we need to go back to the good ole’ Slope Formula and realize that the list of values is really a list of x and y coordinates.

Now let’s plug in the coordinate values (3, 6.26) and (9,3.41) into our slope formula:

Extra Tip! Notice that we added the labels feet/second to our answer. Why does this make sense?? The question tells us that P(t) represents feet and that t is equal to seconds. Another way to look at this question when applying it to the slope formula is to realize that we are finding the change of feet divided by the change of seconds. ____________________________________________________________________________________

Still got questions? Let me know in the comments and as always happy calculating!:)

Looking for the next step? Learn how to graph equation of a line, y=mx+b here!

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How to Factor Quadratic Equations: Algebra

In this post, we are going to dive deep into how to factor Quadratic equations! There are so many different methods to choose from including GCF, Product/Sum, DOTS, and the Quadratic Formula. Here we will go step by step into each method on how to factor quadratic equations, each with their own set of practice questions. For a review on how to factor by grouping, check out this post here and happy calculating! 🙂

Why factor in the first place, you may say? We want to manipulate the equation until we solve for x. Solving for x is our main goal, and factoring allows us to do that. Now let’s get to the good stuff!

How to factor quadratic equations

Greatest Common Factor (GCF):

The greatest common factor is the highest possible number that can be divided out from an equation. This gets the equation into its simplest form and makes it easier for us to solve for x.

Before considering which type of factoring methdo to use, always ask yourself, “Can I take out a GCF?”

How to factor quadratic equations

Product/Sum:

This factoring method is for quadratic equations only! That means the equation takes on the following form:

How to factor quadratic equations

Difference of Two Squares DOTS)

Not to play favorites or anything, but DOTS is the easiest and most lovable of the factoring methods. This factoring method just makes you feel all warm and fuzzy inside or maybe that’s just me). Before we get into how to do DOTS, let’s talk about when?

Quadratic Formula:

We have heard of the quadratic equations, so how id the quadratic formula different?

The Answer: The Quadratic Formula is what we use to factor any trinomial. You can use product/sum on trinomials like we discussed earlier, but this may not always work out easy. The Quadratic Formila on the other hand will work every time!

Low and behold, the Quadratic Formula:

Want more Mathsux? Don’t forget to check out our Youtube channel and more below! And if you have any questions, please don’t hesitate to comment below. Happy Calculating! 🙂

Looking for more on Quadratic Equations and functions? Check out the following Related posts!

Factoring

Factor by Grouping

Completing the Square

The Discriminant

Is it a Function?

Quadratic Equations with 2 Imaginary Solutions

Imaginary and Complex Numbers

Focus and Directrix of a Parabola

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‘Math Suks’ ~ Jimmy Buffett

Need to relax after studying? Close to wanting to “burn your textbook”? This super chill and somewhat cheesy song may help! Coming to you from Jimmy Buffett, the singer has a relaxed, island/ska like vibe to his music. The lyrics come close to sounding like an after school special until the words “Math Sucks” are sung over and over again. Enjoy! 🙂

Click here to listen to the song:

‘Math Suks’ by Jimmy Buffet Lyrics:

If necessity is the mother of invention
Then I’d like to kill the guy who invented this
The numbers come together in some kind of a third dimension
A regular algebraic bliss.

Let’s start with something simple, like one and one ain’t three
Any two plus two will never get you five.
There are fractions in my subtraction and x don’t equal y
But my homework is bound to multiply.

Math suks math suks
I’d like to burn this textbook, I hate this stuff so much.
Math suks math suks
Sometimes I think that I don’t know that much
But math suks.

I got so bored with my homework, I turned on the TV.
The beauty contest winners were all smiling through their teeth.
Then they asked the new Miss America
Hey babe can you add up all those bucks?
She looked puzzled, then just said
“Math Suks”.

Math suks math suks
You don’t even have to spell it,
All you have to do is yell it…
Math suks math suks
Sometime times I think that I don’t know that much
But math suks.

Geometry, trigonometry and if that don’t tax your brain
There are numbers to big to be named
Numerical precision is a science with a mission
And I think it’s gonna drive me insane.

Parents fighting with their children, and the Congress can’t agree
Teachers and their students are all jousting constantly.
Management and labor keep rattling old sabers
Quacking like those Peabody ducks.

Math suks math suks
You don’t even have to spell it,
All you have to do is yell it…
Math suks math suks
Sometime times I think that I don’t know that much
But math suks

Geometry: Congruent Triangles

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Not bad, eh? If there is anything you have questions on please don’t hesitate to ask! 🙂 If you are looking to test out your skills on this topic even more, check out more challenging questions here.

And for more of me and my nerdy math jokes take a look at MathSux on

Twitter and Facebook. Happy calculating! 🙂