Monday, February 4, 2013

Test Review

We have been covering different kinds of factoring, finding the LCM, finding the GCF, word problems and setting equal to zero in class, here is a quick review for our test hope it helps. 

 Factoring by grouping:

 ax - bx + ay - by    =      x(a-b) + y(a-b)   =   (x+y)(a-b)

 We use this when there is four terms. You group with two or sometimes even three terms and try to get a common factor which in this problem was (a-b). 

 Difference of Two Squares:

 x2 - 4 = (a+2)(a-2)

 The formula for this is a2-b2 = (a+b)(a-b).

Trinomial Squares:


x2 + 2xy + y2 = (x+y)2

The formula for this is a2 + 2ab + b2 = (a+b)2 or a2 - 2ab + b2 = (a-b)2 depending if the middle term is positive or negative.

Sum and Difference of Cubes

z3 + y6 =  (z+y2)(z2- zy+b2) Sum of Cubes

z3 - y6 =  (z-y2)(z2+zy+b2) Difference of Cubes

The formula for the sum of cubes is a3+b3 = (a+b)(a2-ab+b2)
While the formula for the difference of cubes is a3-b3 = (a-b)(a2+ab+b2)

Tips for factoring:
  • Always look for GCF (greatest common factor before starting)
  • When you have finished make sure your answer is completely factored

Finding the LCM and GCF

To find the GCF make a factor tree for each of the numbers and then create a ven diagram. Put all the factors they all have in common in the middle. Multiply all the numbers in the middle and this is your GCF coefficient. Next look at the variables and take out the variables they all have in common. In this case they all only have a Y in common. To find the LCM you must multiply all of the numbers in the ven diagram, but make sure not to multiply the numbers in the middle more than once. This number is your coefficient. Now look at the variables and take the all the variables from all of the original numbers and if some of the numbers have the same variable, pick the one with the highest exponent.




Word problems/Setting Equal to zero
Find two numbers differing by 3 and whose product is 88


x2+3x=88

x2+3x-88=0

(x+11)(x-8)=0

x+11=0     x-8=0

x=-11        x=8

x=-11, 8

First factor the equation and then set both factored sets equal to zero and then solve.


Posted by at

3 comments:

  1. AnonymousFebruary 6, 2013 at 1:30 PM

    I liked how you wrote down specific formulas that are needed to solve the problems. But I think it would have helped more if you went step by step explaining what exactly you were doing in the process. And why exactly you were taking that step in the process.

    ReplyDelete
  2. LisaFebruary 24, 2013 at 5:28 PM

    Sebastian, your post is a nice overview of the factoring and solving techniques we covered in this unit. I like that you listed all the formulas; you gave a few examples, but one in each category might have helped readers to remember how they are applied. General quadratic factoring was overlooked. It is covered thoroughly in another post, but mention of it in the review would have been ideal. Finally, your tips offer great advice and your word problem was a good example of both setting one up and using the zero product property. Overall, your post served as a good summary.

    ReplyDelete
  3. AnonymousMarch 27, 2013 at 4:22 PM

    I thought that the process of generating a GCF was very detailed and informative. I also like the headings you used to separate the different kinds of formulas so that the reader would know what to use the formulas for. I think that actually writing the word problem and doing a step-by-step of how to solve it would have been even more helpful, but the rest was great.

    ReplyDelete

Subscribe to: Post Comments (Atom)