Chapter 8 Algebra 1 p 3 Barr 2016 8 1 Monomials Factoring A monomial is in factored form when it is expressed as the product of prime numbers and
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[PDF] Chapter 8: Factoring and Quadratic Equations - Menifee County
OPEN ENDED Name three monomials with a GCF of 6 y 3 Explain your answer 34 WRITING IN MATH Define prime factorization in your own words Explain how
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Chapter 8 KEYWORD: MA7 ChProj Factoring Polynomials 8A Factoring Methods in physics to solve quadratic examples, and answers to your questions
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How to find the roots of a quadratic equation, if they exist Chapter 8: Quadratics 327 8-2 The process of changing a sum to a product is called factoring h Examples of trinomials: 12 3k2 + 5k and x2 15x + 26 8-6 Write the area of the
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NAME Answer heu DATE PERIOD 8-6 wer Joa: (x tuxry) (x + 7yXx-y) Chapter 8 Glencoe Algebra 1 Solve Equations by Factoring Factoring and the Zero Product Property can be used to solve many equations of the form x2 +
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PERIOD Chapter 8 40 Glencoe Algebra 1 Practice Solving x2 + bx + c = 0 Factor each (m - 8v)(m + 7v) Solve each equation Find all values of k so that the trinomial x2 + kx - 35 can be factored using integers -34, -2, 2, 34 32
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Chapter 8 Algebra 1 p 3 Barr 2016 8 1 Monomials Factoring A monomial is in factored form when it is expressed as the product of prime numbers and
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8-1 Practice Monomials and Factoring Factor each monomial completely 1 30d5 8-3 Practice Quadratic Equations: x2 + bx+c=0 Factor each polynomial
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For questions #1-2, tell whether the function is quadratic Explain (8-1) T = 4( 7 5) H = 30ml 4w 14 Solve each quadratic equation by factoring (8-6) 3 mut
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CHAPTER 8 Quadratic Equations Functions and Inequalities Section 8 1 Solving Quadratic Equations: Factoring and Special Forms Solutions to Even-Numbered Exercises 287 20 z 3 8 8 z 3 8z 3 0 8z 3 z 1 0 8 z2 5z 3 0 4 z2 1 4z2 5z 2 2z 1 2z 1 4z2 5z 2 22 z ±12 z ±144 z2 144 18 u 4 u 4 0 0 u 4 u 1 0 u2 5u 4 6 5u u2 10 6 6u u u2 10 6 u 1 u 10 2
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Chapter 8 Algebra 1 p. 1 Barr 2016 Chapter 8: Factoring Polynomials Algebra 1 Mr. Barr Name:____________________________________
Chapter 8 Algebra 1 p. 2 Barr 2016 Schedule Due Homework Lesson/Activity 8.1 Monomials & Factoring 8.2 Using the Distributive Property 8.3 Quadratics in the form x2+bx+c Quiz 8.4 Quadratics in the form ax2+bx+c 8.5 Special Cases Quiz Review Exam Date
Chapter 8 Algebra 1 p. 3 Barr 2016 8.1 Monomials & Factoring A monomial is in factored form when it is expressed as the product of prime numbers and variables, and no variable has an exponent greater than 1. Method: Factor Tree Example 1: Factor the monomial completely 42a3 Factor Tree: Example 2: Factor completely -40x2y3 Try These:
Chapter 8 Algebra 1 p. 4 Barr 2016 Try These: Greatest Common Factor (GCF) The product of the common prime factors is called the greatest common factor (GCF) of the numbers. The greatest common factor is the greatest number that is a factor of both original numbers. Relatively Prime When two or more integers or monomials have no common prime factors and their GCF is 1.
Chapter 8 Algebra 1 p. 5 Barr 2016 8.1 Additional PracticeChapter 8 Algebra 1 p. 6 Barr 2016 8.2 Using the Distributive Property The Distributive Property has been used to multiply a polynomial by a monomial. It can also be used in REVERSE to express a polynomial in factored form. Here is what it looks like: The Method: 1. Find the GCF 2. Write each monomial as a product of the GCF and its remaining factors 3. Reverse the Distributive Property. Write the GCF, and then in parentheses write the sum/difference of the remaining factors. Try These:
Chapter 8 Algebra 1 p. 7 Barr 2016 Factor by Grouping Sometimes when there are 4 monomials we can factor by grouping. The result is the product of two binomials (looks like what we used to FOIL in last chapter). The Method: 1. Split the four terms in half making two mini problems 2. Find the GCF of the first two terms. Then find the GCF of the last two terms. What is left in the parentheses should be identical 3. Write the contents of the identical parentheses (just once). Then in a second set of parentheses write the sum/difference of the remaining factors (the two GCFs you factored out). 4. Check using FOIL Try These:
Chapter 8 Algebra 1 p. 8 Barr 2016 8.2 Additional PracticeChapter 8 Algebra 1 p. 9 Barr 2016 8.3 Quadratics in the form x2+bx+c To factor a trinomial of the form x2 + bx + c, find two integers, m and p, whose sum is equal to b and whose product is equal to c. Try These:
Chapter 8 Algebra 1 p. 10 Barr 2016 8.3 Additional PracticeChapter 8 Algebra 1 p. 11 Barr 2016 8.4 Quadratics in the form ax2+bx+c Overview:To factor a trinomial of the form ax2 + bx + c, find two integers, m and p whose product is equal to ac and whose sum is equal to b. Prime Polynomial A polynomial that cannot be factored Always try and factor out a GCF first! Example 1: If you try to factor out a GCF and can't, or if you factor a factor out a GCF and there is still a number in front of the "x" then follow these rules. The Method: Step One: Try to factor out a GCF Step Two: Find two numbers whose product is a•c and whose sum is b. Step 3: Split up the middle term. Write it as the sum of the two number you found in the last step. Step 4: Factor by grouping Example 2: Try These:
Chapter 8 Algebra 1 p. 12 Barr 2016
Chapter 8 Algebra 1 p. 13 Barr 2016 8.4 Additional PracticeChapter 8 Algebra 1 p. 14 Barr 2016 8.5 Factoring Special Cases Overview: There are two types of special factoring: Difference of Squares and Perfect Squares. Difference of Squares This is the only time we "undo" FOIL when working with a binomial (every other time it is a trinomial). You will recognize it is a difference of squares if both terms are perfect squares and they are separated by a subtraction sign. You can tell you factored it correctly if the two set of parentheses are almost identical except one will have a "+" and the other a "-". The two terms in each set will be the square roots of the original terms, Don't forget to factor out a GCF! Try These:
Chapter 8 Algebra 1 p. 15 Barr 2016 Perfect Squares There is a special pattern that occurs that can help you recognize a perfect square trinomial Factor as normal but your end result should be a binomial squared. Example 1: Try These:
Chapter 8 Algebra 1 p. 16 Barr 2016 8.5 Additional Practicequotesdbs_dbs20.pdfusesText_26