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Chapter 6 Tutorial

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Learn Alegebra 1

Learn Alegebra 1

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  • 1. By Caleb Reagor, Brendan Inson, and Jack Guenther
    Flugenheiman
    (Need Help? Look at vocabulary at very end)
    Chapter 6 Tutorial
  • 2. Chapter Opener
    http://algebraiperiod6.pbworks.com/Flugenheiman-Chapter-6-Opener
  • 3. Section 6.1
    http://algebraiperiod6.pbworks.com/Flugenheiman-Section-1
  • 4. Section 6.2
    In this section you will learn how to factor trinomials with the form of x²+bx+c
    The coefficient will only be 1 for the squared variable
  • 5. Section 6.2
    You may remember that factoring is writing a product into factors
    For example the factors of x²+3x+2 are (x+1) and (x+2)
    x times x equals x² and it can not be x² and 1 because that would get rid of the 3x in the middle
    There is 3x+2 because positive factors of two are 2 and 1 and the sum of them is 3 for the 3x
  • 6. Section 6.2
    Practice Problems
    Factor two binomials out of the problems
    x²+7x+10
    x²+8x+12
  • 7. Section 6.2
    Answers
    (x+5)(x+2)
    (x+2)(x+6)
  • 8. Section 6.2
    There are negatives such as:
    x²-3x+2=(x-2)(x-1)
    x²+1x-2=(x-1)(x+2)
    x²-1x-2=(x+1)(x-2)
    There are some times perfect square trinomials
    x²+2x+1=(x+1)(x+1)=(x+1) ²
  • 9. Section 6.2
    Practice problems
    x²-3x+2
    x²+3x-18
    x²-3x-18
    x²+6x+9
  • 10. Section 6.2
    Answers
    (x-2)(x-1)
    (x+6)(x-3)
    (x+3)(x-6)
    (x+3) ²
  • 11. Section 6.2
    There are also ones with the fourth power
    x⁴+3x²+2=(x²+2)(x²+1)
    There are also ones with two variables
    x²+2xy+y²=(x+y)(x+y) or (x+y)²
  • 12. Section 6.2
    Practice Problems
    x⁴+2x²+1
    x²+4xy+2y²
  • 13. Section 6.2
    Answers
    (x²+1) ²
    (x+2y) ²
  • 14. Section 6.3
    http://voicethread.com/share/947591/
  • 15. Section 6.4
    In this section you will learn how to factor binomials of the form ax²+bx+c by grouping
  • 16. Section 6.4
    Go back to section 6.1 for the basics of factoring ax ²+bx+c with “a”=1
    This section is an extended method of this but to have “a” larger then 1
    An example of this is 6x²+11x+3
    Before you start you always need to see if it is a perfect square trinomial or if it has a greatest common factor- this problem has none
  • 17. Section 6.4
    This is how to solve 6x ²+11x+3
    To solve the problem you multiply 6x ² and 3 to equal 18x²
    You then find factors of 18x² that equal 11x
    9x plus 2x equals 11x; when multiplied, they equal 18x²
  • 18. Section 6.4
    You take those factors and put it into the equation
    So instead of 6x ²+11x+3 you do 6x²+9x+2x+3
    You then group them into groups with greatest common factors; (6x²+9x)+(2x+3)
    Then you factor out the greatest common factors of the grouped parts, try to make the inside problem the same, for example
    (6x ²+9x)+(2x+3)=3x(2x+3)+1(2x+3)
    You then add/subtract the greatest common factors; you then multiply that equation by the other same terms (3x+1)(2x+3)
  • 19. Section 6.4
    Practice Problems
    10x²+21x+2
    6x²+32x+10
    7x²+17x+6
  • 20. Section 6.4
    Answers
    10x²+20x+x+2=(10x²+20x)+(x+2)=10x(x+2)+1(x+2) finally equaling (10x+1)(x+2)
    2(gcf)(3x²+15x+x+5)=2(3x²+x)+(15x+5)=
    2[x(3x+1)+5(3x+1)] finally equaling 2(x+5)(3x+1)
    7x²+14x+3x+6=(7x²+14x)+(3x+6)=7x(x+2)+3(x+2) finally equaling (7x+3)(x+2)
  • 21. Section 6.4
    You can do this for perfect square trinomials and negative problems such as
    4x²-8x+4=(2x-2)² since that this is a prime you do not have to do all of the work
    ax²+bx-c in this you do the same thing you do for a positive number but the final equation looks like this (dx+e)(fx-g) and that is the same for ax²-bx-c but the negative number without a variable is larger then the positive
  • 22. Section 6.4
    Practice Problems
    9x²+12x+4
    8x²+63x-8
    8x²-63x-8
  • 23. Section 6.4
    Answers
    (3x+2)²
    (8x-1)(x+8)
    (8x+1)(x-8)
  • 24. Section 6.5
    http://voicethread.com/share/965601/
  • 25. Vocabulary
    http://algebraiperiod6.pbworks.com/Flugenheiman-Vocabulary