Why Am I Struggling with Polynomials and Rational Expressions in Algebra II?

[Unteroffizier]

Hello.

I am currently studying at a specialized mechanical engineering high school. I'm in my first (or 10th) year, as I've stated before.

I've done algebra I and algebra II, along with about one half of trigonometry (utilizing the trigonometric functions in practical problems, like splitting vectors into two x and y forces, but that's mechanics, another subject) and set theory (plus intervals) so far. It's all been relatively easy, but I'm seriously running into a brick wall here.

I know I said I took algebra II, but that doesn't mean I mastered it. In fact, I'm awful at it. I've got no problem solving equations with one or two unknowns, quadratic equations, sets of equations, graphing functions and quadratic functions, etc.. However, I can't seem to wrap my head around polynomials and rational expressions...

Polynomials I somewhat understand. When they aren't too long and difficult to simplify, I can easily complete them. However, once it involves square root, cube roots, powers and square roots of cube roots (or other nonsensical madness), I simply cannot do it. Maybe it's a mental block, a lack of confidence, I don't know. I just know that it takes me thirty minutes to complete a long polynomial, and I usually make computational or sign errors on the way, rendering my work pointless.

Rational expressions I simply cannot understand. I can't. I don't know how to define them, how to simplify them, how to work with them and I'm sick from looking at them. I just don't know what to do with them at all, and I seriously need help, or at least advice on learning to solve them.

My maths results have been suffering. I'm used to being a grade A or B student, but now my grades seem to be declining exponentially (seriously, the decline grows steeper and steeper as I go. How's that for a lesson in exponential growth). I'd normally wait it out and hope something better comes along, but I don't want to have a gaping hole in my knowledge.

I've got no problem at all with physics problems so far. Kinematics is working fine for me, and it's my best subject at the moment. Mechanics is also fine. It's difficult, and takes time to learn, but I'm somewhat confident in my ability to replace constraints with forces.

Please, no matter how many problems I try to solve, no matter how many videos I watch, I'm just not improving at all. I seriously want to do physics or ME in life, like really badly, but if I can't deal with trivial algebra II, how will I ever deal with calculus?

I don't want my dream to be crushed because of rational expressions. I am in dire need of help.

 

[FactChecker]

You need a tutor that can see what you are doing and spot any misconceptions. Or you might try posting an example problem with your work (in the homework format) and see if someone can help you.

 

[Unteroffizier]

Right. That is true. I have been considering getting a tutor for some time now. I do believe it is the best way to go.

How do I post an example? I would gladly show you a few of my worst nightmares.

 

[FactChecker]

There is a homework / coursework section under Science Education. Follow the format for homework posts and show as much of your work and thinking as you can.

 

[Unteroffizier]

Will do. Thanks!

 

[symbolipoint]

Polynomials I somewhat understand. When they aren't too long and difficult to simplify, I can easily complete them. However, once it involves square root, cube roots, powers and square roots of cube roots (or other nonsensical madness), I simply cannot do it. Maybe it's a mental block, a lack of confidence, I don't know. I just know that it takes me thirty minutes to complete a long polynomial, and I usually make computational or sign errors on the way, rendering my work pointless.

I did not read the responses yet, but maybe intensively review Rules of Exponents, which could help you understand how to work with them better. Polynomials and Rational functions and making mistakes in signs is a normal difficulty and with review, restudy, maybe outside of the regular semester, you could master them or become more comfortable handling them.

 

[symbolipoint]

Please, no matter how many problems I try to solve, no matter how many videos I watch, I'm just not improving at all. I seriously want to do physics or ME in life, like really badly, but if I can't deal with trivial algebra II, how will I ever deal with calculus?

Algebra 2 can be very difficult (for some students). Study ALL of it again on your own, and you may get closer to mastering the topics and skills. One gets better at this with repeated study. Do or start any time you can; it might take three months; or you might spend a whole summer reviewing it.

 

[Unteroffizier]

I certainly hope so. I wish to be educated, and I wish to pass down my knowledge when the time finally comes, and I'd hate to be broken by my mortal enemy without a proper fight. Yes, rational expressions are now my mortal enemy, as they have been ever since the beginning... I'll do my best to revise everything with what little time I have. Suppose I'll have to deal with today's failed test and move on.

Additionally, I'd like to ask if there will be a use for them later on. Polynomials seem useful, but I'm not sure about expressions. Unlike most other things in algebra, I'm not really noticing any practical use for rational expressions. It's probably personal bias, and that's why I need to know for sure. If they do have a use in physics or engineering, that will only motivate me further to master them.

 

[symbolipoint]

A tutor might be good, or you might just need more time regardless of tutor or not a tutor. Just in case you don't have much improvement during the term with a tutor, do not be upset with the tutor - YOU JUST MIGHT NEED MORE TIME TO DEVELOP, and you can.

You are wondering about practical value of polynomials and rational functions. Doing well with them will at least make you stronger mathematically for studying and using Physics and any Engineering. I leave it to other members to say how these mathematics are applied.

 

[member 587159]

I certainly hope so. I wish to be educated, and I wish to pass down my knowledge when the time finally comes, and I'd hate to be broken by my mortal enemy without a proper fight. Yes, rational expressions are now my mortal enemy, as they have been ever since the beginning... I'll do my best to revise everything with what little time I have. Suppose I'll have to deal with today's failed test and move on.

Additionally, I'd like to ask if there will be a use for them later on. Polynomials seem useful, but I'm not sure about expressions. Unlike most other things in algebra, I'm not really noticing any practical use for rational expressions. It's probably personal bias, and that's why I need to know for sure. If they do have a use in physics or engineering, that will only motivate me further to master them.

Well, let's say, that it's quite important to know how to manipulate rational expressions later on.

You will learn how to differentiate/integrate rational functions (and this is important as many physics formulas involve rational functions) and you will need your knowledge to simplify them (in general, the derivative of a rational expression is a rational expression) to find zero's of those functions, etc. Most calculus based books spend many pages on how to integrate rational functions, as there are several methods based on the case.