Podcast
Questions and Answers
What is the placeholder needed when dividing $x^2 - 1$ by $x - 3$?
What is the placeholder needed when dividing $x^2 - 1$ by $x - 3$?
- 0
- 1
- 3x
- -3x (correct)
What is $(x - 3)^3$ expanded?
What is $(x - 3)^3$ expanded?
x^3 - 9x^2 + 27x - 27
What is the expanded form of $3x^2(x + 1)$?
What is the expanded form of $3x^2(x + 1)$?
3x^3 + 3x^2
What is one of the factored forms of $x^3 - 9x^2 + 27x - 27$?
What is one of the factored forms of $x^3 - 9x^2 + 27x - 27$?
The expression $x^2 - 5$ is prime.
The expression $x^2 - 5$ is prime.
When dividing a polynomial by a monomial, each term of the polynomial is divided by the monomial.
When dividing a polynomial by a monomial, each term of the polynomial is divided by the monomial.
What is the result of expanding $(4c + 5m)(4c - 5m)$?
What is the result of expanding $(4c + 5m)(4c - 5m)$?
What is $(2y + 3)^2$ in expanded form?
What is $(2y + 3)^2$ in expanded form?
What is the result of expanding $(w + 12)(w - 12)$?
What is the result of expanding $(w + 12)(w - 12)$?
What do you get when you factor $y^2 - 2y - 4$?
What do you get when you factor $y^2 - 2y - 4$?
Study Notes
Polynomial Division and Properties
- When dividing (x^2 - 1) by (x - 3), a placeholder of (-3x) is necessary for proper alignment.
- Dividing a polynomial by a monomial involves dividing each term of the polynomial individually by the monomial.
Factored Forms and Expansion
- The expression (x^3 - 9x^2 + 27x - 27) can be factored as ((x - 3)^3).
- Expansion of ((2y + 3)^2) results in (4y^2 + 12y + 9).
- The product ((4c + 5m)(4c - 5m)) simplifies to (16c^2 - 25m^2).
- The difference of squares formula is applied to ((w + 12)(w - 12)), resulting in (w^2 - 144).
Prime Expressions
- The expression (x^2 - 5) is considered prime, indicating it cannot be factored over the integers.
Polynomial Simplification
- The expression (y^2 - 2y - 4) can be rewritten as (\frac{y^3 - y^2 - 6y - 4}{y + 1}) showing the polynomial in terms of another variable.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with these flashcards covering key concepts from Abeka Algebra 2 Quiz 2. Each card helps reinforce your understanding of polynomial division and factoring techniques. Get ready to sharpen your algebra skills!
