Intensive Math-Algebra I Mini-Lesson M912.4.3 Summer 2013 Factoring Polynomials Student Packet Day 15
Name: Date: Benchmark M912.4.3 Factor polynomials expressions This benchmark will be assessed using MC items. Students will: Factor polynomials expressions which may include greatest common factor, difference of two squares, and trinomials Content Limits All monomials in items will have, at most, two variables. Coefficients must be integers. In items requiring first factoring the GCF and then factoring the remaining polynomials, the remaining polynomials must have a maximum degree of two. In items that require simplifying algebraic ratios, the following factoring methods may be used: GCF, difference of two squares, and/or trinomials. Response Attributes: Items that include rational expressions should state restrictions to the domain or note that the value of the denominator is not equal to zero. Distractors of rational expression items will not include expressions that are equivalent to the correct answer. Lesson M912.4.3 Textbook: Prentice Hall Algebra 1 I can Factor Polynomial Expressions Vocabulary Trinomial Polynomial Greatest Common Factor (GCF) Difference of Squares Squares of Binomials Essential Understanding Some trinomial of the form or can be factored into equivalent forms that are the product of two binomials. The signs and factors of the coefficients of the trinomials can be factored. Sometimes the GCF of the polynomial should be factored out before the remaining polynomial is factored.
Some trinomials, such as squares of binomials or differences of two squares, can be factored by reversing the rules for multiplying special-case binomials. Example # 1: Textbook page 500 Example # 2: Textbook page 501 Example # 3: Textbook page 501 Example # 4: Textbook page 502 Guided Practice: Textbook page 503: 14 19, and 27-31 Example # 5: Textbook page 506 Example # 6: Textbook page 507 Example # 7: Textbook page 508 Guided Practice: Textbook page 509: 17-24 Example # 8: Textbook page 512 Example # 9: Textbook page 513 Example # 10: Textbook page 513 Example # 11: Textbook page 514 Guided Practice: Textbook page 513: 18 23, page 514: 24 26, and page 515: 52 Guided Practice: Textbook page 271: 16 and 17 Small Group Practice: Focus Practice MA912A43 Mini-Assessment MA912A43 Score: Home Learning: HL MA912A43
Focus Practice M912.4.3 Factor completely the following expressions: 1. 18x 2 y 2 + 36x 3 y 3 27x 3 y 2. x 2 2x 120 3. 36x 100y 2 x 4. 2x 2 + x 28 5. 4a 2 b 12ab + 5a 15 6. 18x 3 y + 24x 2 y 2 12xy 3 7. x 2 + 11x 60 8. 36y 81x 2 y 9. 3x 2 + 13x 10 10. 14m 2 n 3 21mn 2 + 8mn 12
Home Learning M912.4.3: Factoring Polynomials Expressions 1. Factor the expression completely. ) ) ) ) 2. Factor the expression completely. 3. Factor the expression completely. 4. The area of a rectangle is given by function,. Which below are possible expressions for the length and width of the rectangle? 5. The volume of a shipping box can be represented by the expression. Which expressions below are possible dimensions for the box?
6. Factor the expression completely. 7. Johnna says the area of the face of a cube is given by the expression. Is this possible? No, because the expression is not factorable. No, because the factors of the expression are not the same. Yes, because the expression is factorable. Yes, because the factors of the expression are the same. 8. Factor the expression completely. 9. Factor the expression completely. 10. If is one factor of, what is the other factor?