How does factoring work in algebra and why is it important for calculus?

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This means understanding algebra and trigonometry at a high level, because they are the building blocks for calculus concepts. It's not just about memorizing formulas, it's about understanding how to manipulate numbers and equations to solve problems. In summary, the conversation discusses the need to understand factoring in order to solve calculus problems. The speaker expresses frustration with not having paid attention to math in the past and needing to brush up on algebra and trigonometry before tackling calculus. They also mention the importance of understanding the foundations of math in order to succeed in more advanced topics like calculus.
  • #1
Deicider
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Homework Statement



Well,i never paid attention to maths,few things i learned and now i need to solve calculus(dont ask why) but to do that i need to first understand how factoring works,its a basic thing,yes ,i'v missed it and can't go on without it.
2. Relevant equations
Few examples and solutions from the book.
1) x^3-3x^2=x^2(x-3)
2) x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)
3) 4x^2-1=(2x-1)(2x+1)
4) x^3-x=x(x^2-1)=x(x-1)(x+1)

The Attempt at a Solution


I spent few hours to understand them by myself but couldn't.
Can anyone explain in details how exactly this works?
Help the newb.
 
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  • #2
x^3 = x multiplied by x multiplied by x
similarly x^2 is equal to x multiplied by x

so [tex]x^{3} - 3 x^{2} = x. x. x - 3. x. x[/tex]

Take out what is common in between. Here common term is x.x
so x. x can be written as [tex]x^2[/tex]

so it is equal to [tex]x^{2}(x-3)[/tex]

And for all the rest, you have to know one formula

[tex](x^{2} - a^{2}) = (x - a)(x + a)[/tex]

Actually the your problem is so easy that it is difficult for me to tell. And I think that's the reason why nobody has answered it yet. I don't know how to explain such problems but I've tried my best.
 
Last edited:
  • #3
Before you can think of factoring the expression of the left, you should know
how to multiply the factored expression on the right, to get the expression
on the left.
 
  • #4
Deicider said:
Well,i never paid attention to maths,few things i learned and now i need to solve calculus(dont ask why) but to do that i need to first understand how factoring works,its a basic thing,yes ,i'v missed it and can't go on without it.
If you're studying calculus now, and are mystified by factoring, you've really got your work cut out for you. Realistically, you will probably need to spend half or more of your time brushing up on algebra and trig concepts in order just to be able to understand the work shown in examples. And that doesn't include being able to work the problems through from start to finish.

Some people can do this, and some can't, and this depends to a fair degree on their motivation or lack thereof. Unlike some other disciplines, success at one level of mathematics requires a solid understanding of the preceding subjects. You might be able to understand some of the calculus concepts at a high level, but if you can't factor expressions or do the other things that you are expected to have mastered, it's going to be very difficult.
 
  • #5
I'm telling you my way of studying Maths. I never try to understand by looking at the examples. I start solving it, doesn't matter whether i know it or not. and when you'll stuck look at book to know how they had cleared that bump
 
  • #6
The reason why [tex]x^2-a^2=(x+a)(x-a)[/tex] is this:

Let's expand [tex](x+a)(x-a)[/tex]

[tex](x+a)x-(x+a)a[/tex]

[tex]x^2+ax-ax-a^2[/tex]

[tex]x^2-a^2[/tex]

Apply similar ideas to the rest.
 
  • #7
Am failure of digits ,a beggar of numbers ,am a dying equation ;(

Ok now,why maths are separated into pre and post calculus?
I just need to learn algebra first right?
 
  • #8
Deicider said:
Am failure of digits ,a beggar of numbers ,am a dying equation ;(

Ok now,why maths are separated into pre and post calculus?
I just need to learn algebra first right?
Yes, and trigonometry as well. As I said before, in order to succeed in calculus, you first have to have the foundations in place.
 

1. What are factors and how do they affect experiments?

Factors are variables that are intentionally changed or controlled in a scientific experiment. They can include things like time, temperature, or amount of a substance. Factors affect experiments by influencing the outcome and providing valuable data for analysis and interpretation.

2. How do factors impact the validity of an experiment?

The factors used in an experiment can greatly impact its validity. If the factors are not controlled or varied properly, it can lead to inaccurate or biased results. It is important for scientists to carefully consider and control all factors in an experiment to ensure its validity.

3. Can factors be controlled in an experiment?

Yes, factors can and should be controlled in an experiment. This means that they should be carefully monitored and adjusted as needed to ensure that they are not unintentionally influencing the outcome. By controlling factors, scientists can increase the reliability and accuracy of their experiments.

4. How do scientists determine which factors to include in an experiment?

Scientists determine which factors to include in an experiment based on the research question or hypothesis they are testing. They carefully consider which factors may have an impact on the outcome and choose to either control or vary them in the experiment. This decision is based on the specific goals and objectives of the experiment.

5. Can factors be controlled in real-world situations?

In real-world situations, it may be more difficult to control factors as compared to a controlled laboratory setting. However, scientists can still make efforts to control and monitor factors as much as possible to ensure accurate and reliable results. In some cases, scientists may also choose to design experiments that mimic real-world conditions in order to better understand how factors work in these situations.

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