Chapter 6 Tutorial


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Chapter 6 Tutorial

  1. 1. By Caleb Reagor, Brendan Inson, and Jack Guenther<br />Flugenheiman<br />(Need Help? Look at vocabulary at very end)<br />Chapter 6 Tutorial<br />
  2. 2. Chapter Opener<br /><br />
  3. 3. Section 6.1<br /><br />
  4. 4. Section 6.2<br />In this section you will learn how to factor trinomials with the form of x²+bx+c<br />The coefficient will only be 1 for the squared variable<br />
  5. 5. Section 6.2<br />You may remember that factoring is writing a product into factors<br />For example the factors of x²+3x+2 are (x+1) and (x+2)<br />x times x equals x² and it can not be x² and 1 because that would get rid of the 3x in the middle<br />There is 3x+2 because positive factors of two are 2 and 1 and the sum of them is 3 for the 3x<br />
  6. 6. Section 6.2<br />Practice Problems<br />Factor two binomials out of the problems<br />x²+7x+10<br />x²+8x+12<br />
  7. 7. Section 6.2<br />Answers<br />(x+5)(x+2)<br />(x+2)(x+6)<br />
  8. 8. Section 6.2<br />There are negatives such as:<br />x²-3x+2=(x-2)(x-1)<br />x²+1x-2=(x-1)(x+2)<br />x²-1x-2=(x+1)(x-2)<br />There are some times perfect square trinomials<br />x²+2x+1=(x+1)(x+1)=(x+1) ²<br />
  9. 9. Section 6.2<br />Practice problems<br />x²-3x+2<br />x²+3x-18<br />x²-3x-18<br />x²+6x+9<br />
  10. 10. Section 6.2<br />Answers<br />(x-2)(x-1)<br />(x+6)(x-3)<br />(x+3)(x-6)<br />(x+3) ²<br />
  11. 11. Section 6.2<br />There are also ones with the fourth power<br />x⁴+3x²+2=(x²+2)(x²+1)<br />There are also ones with two variables<br />x²+2xy+y²=(x+y)(x+y) or (x+y)²<br />
  12. 12. Section 6.2<br />Practice Problems<br />x⁴+2x²+1<br />x²+4xy+2y²<br />
  13. 13. Section 6.2<br />Answers<br />(x²+1) ²<br />(x+2y) ²<br />
  14. 14. Section 6.3<br /><br />
  15. 15. Section 6.4<br />In this section you will learn how to factor binomials of the form ax²+bx+c by grouping<br />
  16. 16. Section 6.4<br />Go back to section 6.1 for the basics of factoring ax ²+bx+c with “a”=1<br />This section is an extended method of this but to have “a” larger then 1<br />An example of this is 6x²+11x+3<br />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<br />
  17. 17. Section 6.4<br />This is how to solve 6x ²+11x+3<br />To solve the problem you multiply 6x ² and 3 to equal 18x²<br />You then find factors of 18x² that equal 11x<br />9x plus 2x equals 11x; when multiplied, they equal 18x²<br />
  18. 18. Section 6.4<br />You take those factors and put it into the equation<br />So instead of 6x ²+11x+3 you do 6x²+9x+2x+3<br />You then group them into groups with greatest common factors; (6x²+9x)+(2x+3)<br />Then you factor out the greatest common factors of the grouped parts, try to make the inside problem the same, for example<br />(6x ²+9x)+(2x+3)=3x(2x+3)+1(2x+3)<br />You then add/subtract the greatest common factors; you then multiply that equation by the other same terms (3x+1)(2x+3) <br />
  19. 19. Section 6.4<br />Practice Problems<br />10x²+21x+2<br />6x²+32x+10<br />7x²+17x+6<br />
  20. 20. Section 6.4<br />Answers<br />10x²+20x+x+2=(10x²+20x)+(x+2)=10x(x+2)+1(x+2) finally equaling (10x+1)(x+2)<br />2(gcf)(3x²+15x+x+5)=2(3x²+x)+(15x+5)=<br />2[x(3x+1)+5(3x+1)] finally equaling 2(x+5)(3x+1)<br />7x²+14x+3x+6=(7x²+14x)+(3x+6)=7x(x+2)+3(x+2) finally equaling (7x+3)(x+2)<br />
  21. 21. Section 6.4<br />You can do this for perfect square trinomials and negative problems such as <br />4x²-8x+4=(2x-2)² since that this is a prime you do not have to do all of the work<br />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<br />
  22. 22. Section 6.4<br />Practice Problems<br />9x²+12x+4<br />8x²+63x-8<br />8x²-63x-8<br />
  23. 23. Section 6.4<br />Answers<br />(3x+2)²<br />(8x-1)(x+8)<br />(8x+1)(x-8)<br />
  24. 24. Section 6.5<br /><br />
  25. 25. Vocabulary<br /><br />