Questions and Answers
What are the two methods to find the prime factorization of a number?
Factor tree, Ladder diagram
Find the prime factorization of 40.
2³ * 5
Find the prime factorization of 17.
17
What are the two methods to find the GCF of a pair of numbers?
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Find the GCF of 12 and 16.
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How do you find the GCF of a pair of monomials?
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Find the GCF of 6x² and 7y³.
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Find the GCF of 18x² and 27x³.
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What property states that a(b+c) = ab + ac?
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What happens to the distributive property when you factor by GCF?
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What are the steps to factoring using the GCF?
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Factor 8x³ - 4x² - 16x by GCF.
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What are the steps to factoring by grouping?
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Factor 6x⁴ - 4x³ + 12x - 8 by grouping.
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What happens when you factor two quantities that are opposites?
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Factor 15x² - 10x³ + 8x - 12.
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What is the form to factor a trinomial?
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Factor x² - 4x - 32.
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Factor 20x² + 21x - 5.
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What is a polynomial?
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What is a monomial?
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What is a binomial?
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What is a trinomial?
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What are factors?
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What does it mean to factor?
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What is the Greatest Common Factor (GCF)?
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What is the Zero Product Property?
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Study Notes
Prime Factorization
- Two methods: Factor tree and Ladder diagram.
- Example: Prime factorization of 40 is (2^3 \times 5) or (5 \times 2 \times 2 \times 2).
- Prime factorization of 17 is simply 17 or (17 \times 1).
Greatest Common Factor (GCF)
- Two methods to find GCF: List the factors or use Prime Factorization.
- GCF of 12 and 16 is 4, derived from their factor lists.
- For monomials, find the GCF by:
- Writing prime factorizations of coefficients.
- Aligning common factors.
- Multiplying the common factors.
GCF Examples
- GCF of (6x^2) and (7y^3) is 1 (no common factors).
- GCF of (18x^2) and (27x^3) is (9x^2).
Properties
- Distributive Property: (a(b+c) = ab + ac).
- Factoring by GCF reverses the distributive property: (xy + xz = x(y+z)).
Factoring Techniques
- Steps for factoring using GCF:
- Find the GCF of the polynomial terms.
- Write terms as products using the GCF.
- Apply the Distributive Property to factor out the GCF.
- Verify the answer.
- Example of factoring (8x^3 - 4x^2 - 16x) yields (4x(2x^2 - x - 4)).
Factoring by Grouping
- Steps for factoring by grouping:
- Group terms with common factors.
- Factor out the GCF from each group.
- Factor out the common binomial factor.
- Check solution.
- Example: Factoring (6x^4 - 4x^3 + 12x - 8) results in ((3x - 2)(2x^3 + 4)).
Special Cases
- When factoring two opposing quantities, the sum is 0.
- Example: Factoring (15x^2 - 10x^3 + 8x - 12) results in ((3 - 2x)(5x^2 - 4)).
Trinomials and Polynomial Types
- Standard form for factoring a trinomial: (x^2 + bx + c).
- Example: Factoring (x^2 - 4x - 32) gives ((x - 8)(x + 4)).
- Example: Factoring (20x^2 + 21x - 5) results in ((4x + 5)(5x - 1)).
Definitions
- Polynomial: Combination of terms through addition or subtraction.
- Monomial: One-term expression (number, variable, or product).
- Binomial: Polynomial consisting of two terms.
- Trinomial: Polynomial consisting of three terms.
- Factors: Elements being multiplied in an expression.
- GCF: Largest common factor among terms.
- Zero Product Property: If a product equals zero, at least one factor must be zero.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of factoring polynomials with these flashcards. This quiz includes methods like factor trees and ladder diagrams, as well as finding GCFs and prime factorizations. Perfect for Algebra 1 students looking to reinforce their knowledge.