Understanding Polynomials: A Simple Guide for Kids

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elle

11/09/2023

Maths

Polynomial division

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Maths

Pure maths

Algebra & functions

Understanding Polynomials: A Simple Guide for Kids

Understanding polynomials in algebra forms the foundation of advanced mathematical concepts and problem-solving techniques.

Polynomials are mathematical expressions containing constants, variables, coefficients, and non-negative exponents, combined through basic operations
The algebraic long division step-by-step guide demonstrates how to split polynomials into factor pairs
Identifying monomials, binomials, and trinomials helps classify polynomials based on their number of terms
The process involves systematic steps including division, multiplication, and subtraction operations
Understanding polynomial division is crucial for factorization and handling improper fractions

11/09/2023

algebraic (polynomial)
division
WHAT ARE POLYNO MIALS ?
Polynomial originates from the word poly meaning mony and nomial meaning tems.
Polyn

Algebraic Long Division Fundamentals

The algebraic long division step-by-step guide introduces a systematic method for dividing polynomials.

Definition: Algebraic long division is a technique used to split polynomials into factor pairs, with or without remainders.

Example:

x³ + x² - x - 1 splits into $x+1$ $x² +1$ without remainder
x³ + 2x² + 3x + 4 splits into $x-1$ $x² + 3x + 6$ with remainder +10

Highlight: This method is particularly useful for factorizing polynomials and handling improper fractions.

View

Division Process Part 1

The detailed process of polynomial division follows a structured approach similar to regular long division.

Example: Dividing x³ + 6x² + 11x + 6 by x + 2

Step-by-step process:

Arrange the division in "bus shelter" format
Divide the highest power terms
Multiply the divisor by the result
Subtract to find the new dividend

Highlight: The organization of terms in descending order of exponents is crucial for successful division.

View

Division Process Part 2

The continuation of the polynomial division process focuses on the systematic reduction of terms.

Vocabulary: The dividend refers to the polynomial being divided, while the divisor is the polynomial doing the dividing.

Example: Continuing with x³ + 6x² + 11x + 6 ÷ $x + 2$

After initial subtraction, work with 4x² + 11x + 6
Divide 4x² by x to get 4x
Multiply $x + 2$ by 4x

View

Division Process Part 3

The final stages of polynomial division involve careful attention to remaining terms and verification.

Highlight: Each step reduces the degree of the polynomial until reaching the final result.

Example: The process continues until reaching the final terms:

Working with 3x + 6
Dividing by the divisor
Performing final calculations

View

Final Steps and Verification

The completion of polynomial division requires careful attention to detail and verification of results.

Highlight: The final answer should be verified by multiplying the quotient by the divisor and adding any remainder.

Example: The complete division process yields:

Quotient: x² + 4x + 3
Each step systematically reduces the polynomial's degree
Final verification ensures accuracy of the result

View

Additional Example Problem

The sixth page presents another example of polynomial division, reinforcing the concepts through practice.

Example: Division of 2x³ - 9x² + 3x + 4 by x - 4

Highlight: The solution demonstrates:

Systematic application of division steps
Careful handling of negative terms
Verification of zero remainder

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Subjects

Maths

Pure maths

Algebra & functions

Maths

•

147

•

11 Sept 2023

•

7 pages

Understanding Polynomials: A Simple Guide for Kids

elle

@elle.xox

Understanding polynomials in algebra forms the foundation of advanced mathematical concepts and problem-solving techniques.

Polynomials are mathematical expressions containing constants, variables, coefficients, and non-negative exponents, combined through basic operations
The algebraic long division step-by-step guidedemonstrates how to split polynomials... Show more

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Algebraic Long Division Fundamentals

The algebraic long division step-by-step guide introduces a systematic method for dividing polynomials.

Definition: Algebraic long division is a technique used to split polynomials into factor pairs, with or without remainders.

Example:

x³ + x² - x - 1 splits into $x+1$ $x² +1$ without remainder
x³ + 2x² + 3x + 4 splits into $x-1$ $x² + 3x + 6$ with remainder +10

Highlight: This method is particularly useful for factorizing polynomials and handling improper fractions.

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Division Process Part 1

The detailed process of polynomial division follows a structured approach similar to regular long division.

Example: Dividing x³ + 6x² + 11x + 6 by x + 2

Step-by-step process:

Arrange the division in "bus shelter" format
Divide the highest power terms
Multiply the divisor by the result
Subtract to find the new dividend

Highlight: The organization of terms in descending order of exponents is crucial for successful division.

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Division Process Part 2

The continuation of the polynomial division process focuses on the systematic reduction of terms.

Vocabulary: The dividend refers to the polynomial being divided, while the divisor is the polynomial doing the dividing.

Example: Continuing with x³ + 6x² + 11x + 6 ÷ $x + 2$

After initial subtraction, work with 4x² + 11x + 6
Divide 4x² by x to get 4x
Multiply $x + 2$ by 4x

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Division Process Part 3

The final stages of polynomial division involve careful attention to remaining terms and verification.

Highlight: Each step reduces the degree of the polynomial until reaching the final result.

Example: The process continues until reaching the final terms:

Working with 3x + 6
Dividing by the divisor
Performing final calculations

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Final Steps and Verification

The completion of polynomial division requires careful attention to detail and verification of results.

Highlight: The final answer should be verified by multiplying the quotient by the divisor and adding any remainder.

Example: The complete division process yields:

Quotient: x² + 4x + 3
Each step systematically reduces the polynomial's degree
Final verification ensures accuracy of the result

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Additional Example Problem

The sixth page presents another example of polynomial division, reinforcing the concepts through practice.

Example: Division of 2x³ - 9x² + 3x + 4 by x - 4

Highlight: The solution demonstrates:

Systematic application of division steps
Careful handling of negative terms
Verification of zero remainder

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Understanding Polynomials

The foundation of identifying monomials, binomials, and trinomials begins with understanding their basic structure and components.

Definition: Polynomials are mathematical expressions containing constants, variables, coefficients, and exponents $≥0$ , combined through addition, subtraction, or multiplication.

Vocabulary: The term "polynomial" derives from "poly" $many$ and "nomial" $terms$ .

Example:

76 is a monomial $single term$
2x + 6 is a binomial $two terms$
3x² + 2x + 6 is a trinomial $three terms$

Highlight: A crucial rule is that polynomials can never involve division by variables.

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Understanding Polynomials: A Simple Guide for Kids

Algebraic Long Division Fundamentals

Division Process Part 1

Division Process Part 2

Division Process Part 3

Final Steps and Verification

Additional Example Problem

Similar content

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Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

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#1

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Still not convinced? See what other students are saying...

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

The app is very simple and well designed. So far I have always found everything I was looking for :D

I love this app ❤️ I actually use it every time I study.

Understanding Polynomials: A Simple Guide for Kids

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Algebraic Long Division Fundamentals

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Division Process Part 1

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Division Process Part 2

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Division Process Part 3

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Final Steps and Verification

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Additional Example Problem

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Understanding Polynomials

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