Intro to factors & divisibility | Mathematics II | High School Math | Khan Academy

TL;DR

Factors and divisibility concepts from whole numbers extend to algebraic expressions and polynomials.

Transcript

• [Voiceover] You're probably familiar with the general term factor. So if I were to say: What are the factors of 12, you could say: Well what are the whole numbers that I can multiply by another whole number to get 12? So for examples, you could say things like, well I could multiply one times 12 to get 12. So you could say that one is a factor of... Read More

Key Insights

• 😑 Factors in algebra can be expressed using monomials, binomials, or polynomials.
• 😑 Multiplying two algebraic expressions can result in a factorization relationship.
• 😑 Divisibility in algebra determines if one expression can evenly divide another.
• 😑 The concept of factors and divisibility applies to whole numbers, algebraic expressions, and polynomials.
• 🧑‍🏭 Integer coefficients are necessary for determining factors and divisibility in algebra.
• 😑 Understanding factors and divisibility in algebra is essential for simplifying expressions and solving equations.
• 🧑‍🏭 Factors can be found by factoring algebraic expressions using algebraic techniques.

Questions & Answers

Q: What are factors and how do they relate to whole numbers?

Factors are whole numbers that can be multiplied by another whole number to obtain a given number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Q: How does factorization extend to algebraic expressions?

In algebra, factors can also refer to algebraic expressions that, when multiplied, produce another expression. For example, 3xy can be a factor of -6x^3y^4.

Q: What is the relationship between divisibility and factors in algebra?

Divisibility in algebra involves determining if one algebraic expression is a factor of another. For example, X + 3 is a factor of X^2 + 10x + 21.

Q: Can factors and divisibility concepts be applied to polynomials?

Yes, factors and divisibility concepts extend to polynomials as well. Polynomials can have factors that divide evenly into them, just like whole numbers and algebraic expressions.

Summary & Key Takeaways

• Factors are the whole numbers that can be multiplied by another whole number to obtain a given number.

• Divisibility in algebra involves determining if one algebraic expression is a factor of another.

• This concept applies not only to monomials but also to binomials and polynomials.