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Factoring

Factoring. How to’s Created by Claudia R. Carter. GCMF (Greatest Common Monomial Factor ). Example : Question : What are the largest number factor and the largest variable(s) that divide evenly into each term? Answer :

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Factoring

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  1. Factoring How to’s Created by Claudia R. Carter

  2. GCMF (Greatest Common Monomial Factor) • Example: • Question: What are the largest number factor and the largest variable(s) that divide evenly into each term? • Answer: • Action: Factored form..... • Note: Sometimes entire parentheses can be “in common”. • Example: ax + by + ay + bx = a(x+y) + b(x+y) = (x+y)(a+b)

  3. . Difference of Two Squares (Square - Square) • Example: • Question: Do I have a perfect square term minus a perfect square term? YES! • Action: Write two parentheses. Put a “+” in one and a “_” in the other. Take the square root of each of the original two squares. • Note: The square of a variable with an exponent is an even number. The square root is half of the power, since when you multiply like bases you add exponents.

  4. Trinomial Square • Example: • Question: How do I identify a trinomial square? Answer: Are the first and third terms perfect squares? Is the second operation “+”? Is the middle term two times the product of the square roots of the first and third terms? YES to all! • Action: Write one parenthesis and square it. • Use the first operation sign. Take the square roots of the first and third terms.

  5. Sum of Difference of Two Cubes (Cube  Cube) • Example: • Question: How do I determine what perfect cubes are? Answer: For numbers becoming familiar with cubes is very helpful. For variables, the powers need to be multiples of 3! • Action: Write two parentheses, one is a binomial and the other is a trinomial. The binomial consists of the cube root of the first term, the operation sign, and the cube root of the second term. The trinomial is based upon the binomial..... something fondly known as SOPPS! (Square the first #, Opposite sign, Product of the the two numbers, Plus, Square of the second #) • Note: Both sum or difference can be used for CUBES!!!!

  6. Table of Squares & Cubes

  7. Coefficient of One ...Form • Example 3:Example 4: • Example 1:Example 2: • Questions: For #1 & 2, What do I multiply to get the third term and ADD to get the middle term? • For #3 & 4, What do I multiply to get the third term and SUBTRACT to get the middle term? * larger number

  8. Coefficient of One • Action: Write two parentheses and use the sign chart from previous slide and answer the questions. • Answer 1: Answer 2: • Answer 3: Answer 4:

  9. Coefficient Other Than One..... Form Example: multiply = ac add to = b Action: TIC TAC TOE multiply = 24 and add = 10 ????

  10. Coefficient Other Than One..... now two factors of 6? now finish the missing factors of 4 Answer: Diagonals

  11. Let’s Practice!

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