Chapter 8: Factoring Polynomials. Algebra 1 Mr. Barr
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1 p. 1 Chapter 8: Factoring Polynomials Algebra 1 Mr. Barr Name:
2 p. 2 Date Schedule Lesson/Activity 8.1 Monomials & Factoring 8.2 Using the Distributive Property 8.3 Quadratics in the form x 2 +bx+c Quiz 8.4 Quadratics in the form ax 2 +bx+c 8.5 Special Cases Quiz Review Exam Homework Due
3 p 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 42a 3 Factor Tree: Example 2: Factor completely -40x 2 y 3 Try These:
4 p. 4 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. Try These:
5 p Additional Practice
6 p 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:
7 p. 7 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:
8 p Additional Practice
9 p Quadratics in the form x 2 +bx+c To factor a trinomial of the form x 2 + bx + c, find two integers, m and p, whose sum is equal to b and whose product is equal to c. Try These:
10 p Additional Practice
11 p Quadratics in the form ax 2 +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:
12 p. 12
13 p Additional Practice
14 p 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:
15 p. 15 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:
16 p Additional Practice
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