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Factoring Monomials

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Factoring Monomials

Study Guide

Key Definition

The prime factorization of a monomial is an expression of its prime numbers, single variables, and if the monomial is negative, the factor $-1$.

Important Notes

A prime number is only divisible by $1$ and itself.
The number $26$ can be factorized as $13 \times 2$.
Factoring involves breaking down into prime factors.
Variables in monomials can also be factored.
Negative coefficients include $-1$ as a factor.

Mathematical Notation

$\times$ represents multiplication

$\div$ represents division

$x^2$ represents x squared

Remember to use proper notation when solving problems

Why It Works

Factoring monomials simplifies expressions, making them easier to work with by utilizing their prime components.

Remember

Every integer greater than 1 is either a prime number or can be expressed as a product of prime numbers.

Quick Reference

Fundamental Theorem of Arithmetic:Each integer greater than 1 is either prime or a product of primes.

Understanding Factoring Monomials

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Video explanation of this concept

Beginner

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Beginner Explanation

Factoring a monomial means expressing it as a product of its prime number factors and its variable factors. For example, factoring $12x$ gives $2 \times 2 \times 3 \times x$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the prime factorization of $60$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $90$ candies to distribute, factorize the number to find a fair distribution.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the monomial $-45x^2y$. What are its prime factors?

Challenge Quiz

Single Choice Quiz

Advanced

Factorize the monomial $100x^3y^2$.

Recap

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Review key concepts and takeaways