Questions and Answers
What is the process of finding products of binomials using short methods called?
Special Products
What is it called when a polynomial is rewritten as a product of polynomial factors?
Factoring polynomials
Which of the following is NOT a method of factoring?
What does GCF stand for in the context of polynomials?
Signup and view all the answers
Determine the GCF of the numbers 20, 24, and 56.
Signup and view all the answers
What is the GCF of the polynomials 12a2b3c3, 24ab4c, and 18a4b2c2?
Signup and view all the answers
Factoring is the reverse of finding the __________.
Signup and view all the answers
Which of these methods can be used to find the GCF of several numbers?
Signup and view all the answers
What should you check first when factoring a polynomial?
Signup and view all the answers
The process of rewriting a polynomial as a product of polynomial factors is called factoring polynomials.
Signup and view all the answers
In the expression (x + 8)(x - 8), what type of product is represented?
Signup and view all the answers
Study Notes
Special Products and Factoring
-
Special products involve efficient methods to find binomial products, including:
- Square of a binomial
- Cube of a binomial
- Product of a sum and difference
-
Factoring is rewriting a polynomial as a product of its polynomial factors, essential methods include:
- Difference of two squares
- Sum and difference of two cubes
- Factoring quadratic trinomials (ax² + bx + c)
- Factoring by grouping
Objectives
- Determine the greatest common monomial factor (GCMF) of a polynomial.
- Recall methods to find the greatest common factor (GCF) of whole numbers.
- Solve problems related to factoring the GCMF.
Factoring Polynomials
- Factoring involves identifying constants, variables, or combinations that compose a polynomial.
- The initial step is determining if the polynomial has a GCMF.
Finding the GCF
- Listing Method example with numbers 20, 24, and 56 shows GCF is 4.
- Continuous division can also find GCF; for those same numbers, it results in 2 x 2 = 4.
- GCMF exercises include:
- x³y²z³, x⁴y⁵z, x²y²z yields GCF = x²y²z.
- Practice with expressions like a⁴b², ab⁴c; m³n²o, m²n⁴, m²n⁵o.
Distributive Property Applications
- Use distributive property to simplify expressions like:
- x² + 2x = x(x + 2)
- 6x³ - 10x² = 2x²(3x - 5)
Examples of Factoring Polynomials
- GCF and Factored Form:
- For 4x² + 6x, GCF = 2x → 2x(2x + 3).
- For 6x⁴ - 14x², identify GCF and simplify.
Factoring Examples
- Example of factoring: 15x³y - 10x²y² = 5x²y(3x - 2y).
- Another example: 8a³(x+y)³ + 12a²(x+y)⁵ results in GCF = 4a²(x+y)³[2a + 3(x+y)²].
Practice Problems
- Factor the following polynomials:
- 6x³ - 5x² + 2x
- 40a³b²c⁷ - 20a⁴bc + 100b⁵c⁴
Difference of Two Squares
- Recognize polynomials that can be simplified using the difference of two squares, e.g.,
- (x + 8)(x - 8) = x² - 64.
Additional Notes
- Review multiplication of polynomials to solidify understanding of products leading to polynomials.
- Announcements for assessments and preparation strategies are essential for a successful study plan.
Study Recommendations
- Review pages on factoring polynomials and strategies.
- Stay updated on quiz dates and ensure material is studied in advance for assessments.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Explore the essential concepts of special products and factoring in this quiz designed for 8th-grade mathematics. You'll learn about key methods such as the square and cube of a binomial, as well as the product of a sum and difference. Test your understanding and enhance your skills in polynomial factoring.
