Многочлены. Арифметические операции над многочленами

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Многочлены. Арифметические операции над многочленами

The Personal SWOT Analysis will provide insights based on your personality strengths and weaknesses, challenges you see ahead, opportunities present around you now, as well as future favorable circumstances.

Деление многочлена на одночлен

разделить отдельно каждый одночлен исходного многочлена на одночлен по правилу деления одночленов. Сложить полученные результаты деления одночленов (то есть записать друг за другом с учетом правила знаков)

Умножение многочлена на многочлен

Finally, look at any threats to your career growth. This part accounts for the external factors that could hurt the chances of attaining your goals.

каждый одночлен первого многочлена умножить на каждый одночлен второго многочлена. Полученные произведения сложить (то есть записать друг за другом с учетом знаков полученных при умножении)

Performing this analysis will often provide key information – it can point out what needs to be done and put problems into perspective.

These are sample questions and sample answers, please feel free to add your own questions and answers.

(a²+ab+b²)(a−b)= =a²·a−a²·b+ab·a−ab·b+b2·a−b²·b= =a²+1−a²b+a¹+1b−ab¹+1+b²a-b²+1= =a³−a²b+a²b−ab²+ab²−b³=a³−b³

(a−b)(−a−2)=a·(−a)−2a+ab+2b=−a²−2a+ab+2b

Формулы сокращенного умножения

For the opportunities section, look at the external factors you can take advantage of in pursuing a promotion, finding a new job or determining a direction for your career.

Квадрат суммы

'Technology' is not equal to Information Technology. For example, if you are in the soap-making business and you bring machines that speed up the process, you have introduced new technology or a process.

• Is the process you currently follow going to change?
• What changes do you need to make in the current process to improve it?
• How much time will you need to learn the new technology?

Add some questions and answers related to your industry and niche.

(a+b)²=a²+2ab+b²

Квадрат разности

(a-b)²=a²-2ab+b²

Разность квадратов

If you plan on changing your job or investing in your own business:

• Is this the right time to invest in your business?
• Will you get your desired salary if you change your job right now?
• Will you get the desired ROI if you invest right now?

Have you calculated the risk involved?

Add a few questions and answers of your own related to the industry that you work in.

a²-b²=(a+b)(a-b)

Основные понятия

Once you have listed out your SWOT - It's now time to evaluate and determine further steps that need to be taken in order to achieve your goals.

There are mainly two methods:
1) Matching
2) Turning negatives into positives

стандартный вид

The other method is converting your weaknesses into strengths or threats into opportunities.

For example: growing a skill set through education, finding a creative way to feature a weakness as a strength, etc.

m²-2mn+n²-m²-2mn-n²=-4mn

3a²x+3ax²+5a⁴-3ax²-8a²x-10a⁴=-5a²x-5a⁴

многочлен

You can evaluate your results using the matching method, which means connecting two of the categories to determine a course of action.

Please see a few examples here.

Трёхчлен

Matching weaknesses to threats exposes areas you should work on or situations to avoid, letting you know where to be more defensive as well.

a²-2ab+b²

a⁴+6a²b+9b²

Двучлен

For example matching strengths to opportunities shows you where to be aggressive and take action.

ab-3c

Вынесение общего множителя за скобки

Примеры

a²(x+y)+b³(x+y)=(x+y)(a²+b³)

2x²y²−2x⁴y²+6x³y³=2x²y²(1−x²+3xy)

Вычисляем многочлен, который остается в скобках

Работаем с буквенными множителями. Находим буквенные множители, которые повторяются в каждом одночлене. Выносим их за скобку в наименьшей степени.

Работаем с числовыми коэффициентами. Находим число, на которое делятся без остатка числовые коэффициенты каждого одночлена.

Умножение многочлена на одночлен

This part examines the areas which you need to improve and the things that will set you back in your career.

It is really important to be honest when you list out your weaknesses.

Чтобы умножить многочлен на одночлен, нужно каждый член многочлена умножить на этот одночлен с учетом правила знаков

xyz(x^2+2y²−3z²)=xyz·x²+xyz·2y²−xyz·3z²= x²+1yz+2xy²+1z-3xyz²+1 =x³yz+2xy³z−3xyz³

Ask people around you about your weaknesses - such as the colleague sitting next to you, your sibling or your best friend.

−4a(−a+b)=(−4a)·(−a)−4ab=4a·a-4ab= =4a¹+1−4ab=4a²−4ab

Do you have stage fright? Or do you become nervous and sweaty when you give a presentation in a room full of people staring at you?

That is something you should definitely work on!

List out such things that you need to improve.

6a(3a−b)=6a·3a−6ab=18a¹+1−6ab=18a²−6ab

Have you ever heard a mother yell at her kid 'Get off your phone or I will throw that phone away'?

Again, be honest and list out all those negative work habits that you have. Your parents/wife/husband/colleagues might help you correctly point them out if you are stuck!

Сложение и вычитание многочленов

Begin by identifying your strengths. These are the traits or skills that set you apart from others.

List out all your strengths - if you get stuck, talk to people around you and ask for their input. Please be honest with yourself.

Порядок выполнения

These are sample questions and sample answers, please feel free to add your own questions and answers.

Выполнить сложение(вычитание)

Skills that you are naturally born with

Have you ever heard someone say 'you are as hard-working as your dad'?

If you are unable to point them out, ask people around you, most likely someone from your family will be able to tell you your Natural Talents.

Choose from the examples below or/and add others:

=x+4

привести подобные

What are the Skills that you have developed over time?

These are the skills you have learned because you view them as essential OR people advised you to acquire them in order to improve yourself.

Choose from the examples below or add others:

=4x−3x−1+5=

Раскрыть скобки

This is something that you learn unconsciously OR you learn by just observing someone you look up to (family/ colleagues/ teachers etc.)

Take a deep breath, close your eyes, think for a minute and type in your 'Natural Strengths' here.

Choose from the examples below or/and add others:

(4x−1)+(5−3x)=4x−1+5−3x=