Factoring polynomial with common monomial factor
- 1. FACTORING POLYNOMIAL WITH COMMON MONOMIAL FACTOR Prepared by: Jimar Mucha
- 2. • The GCF (greatest common factor) of two or more monomials is the product of all their common prime factors. For example, the GCF of 6x, and 4x² is 2x • The distributive property: a(b+c)=ab+ac • To understand how to factor out common factors, we must understand the distributive property.
- 4. • The correct answer is letter B • Based on previous slide we’re going to distribute 2x to 3x and 5
- 5. So the factor of 2x³ and 6x² is 2x²
- 6. • Common monomial factoring is the process of writing a polynomial as a product of two polynomials, one of which is a monomial that factors each term of the polynomial. • Every expression has itself and the number 1 as a factor. These are called the trivial factors. If a monomial is the product of two or more variables or numbers, then it will have factors other than itself and 1.
- 7. ACTIVITY • Identify the common term of each polynomial through prime factorization. 1. 2ab + 2ac – 2a 2. 20x2 – 12 3. x(a-b) + y(a-b) • Ask the following:What are the prime factors of each term? • What is the common factor? • How did you identify the common factor?
- 8. ACTIVITY: MATCH IT TO ME A. 1. x³y² +xy³+ 2x²y³ 2. x³ + x²y + xy² 3. 3y² - 15y - 12 B. a. xy²(x² + y + 2xy) b. 3(y² – 5y – 4) c. xy(x² + x + y)
- 9. ACTIVITY: GROUP ACTIVITY • Cite one real-life situation that demonstrates polynomial with common monomial factor.
- 10. Example: • Find the area of a rectangle whose width is 2x – 3 and the length is 5 more than the width.
- 11. GENERALIZATION • What is a polynomial? • How can we obtain the factors of polynomials using common monomial factor? • What concepts have you learned from factoring that can be applied in your daily living?
- 12. INDIVIDUAL WORK Instructions: Find the GCF of the following monomials 1.Ax⁴, -a²x^6, a³x² 2.56x2, -4x, -12 3.Abx2, -axz, bxy Factor the following polynomials. 4. 5y2 + 10 5. 14p2 + 21