Math Studies II Factoring and Simplifying (November 1, 2010)

First to post this month! Ha!!!!!

On to the blog.....

Math Studies II (11/1/10)

Bellringer:

• Simplify:

1. -3(4x)

2. (x-5)(x+2)

3. (x-5)(x2+4x+14)

• Solutions:

1. -3*4x = 12x

2. x2+2x-5x-10 = x2-3x-20

3. x3+4x2+14x-5x2-20x+70 = x3-1x2-6x+70

• Factor:

1. (x2-9)

2. x2+8x+16

3. x2-5x+14

• Solutions:

1. (x-3)(x+3)

2. (x+4)(x+4)

3. (x-7)(x+2)

Explanation of Solutions:

Example 1: (x2-9) First, what two numbers will equal -9 when multiplied?.... hmmm? Hey, How about 3 and -3. That works. So next we check to see if (x+3) multiplied by (x-3) equal (x2-9) by using the foil method......and (x+3)(x-3)= x2-9

Example 2: x2-5x+14. First, find two numbers that multiply to make -14 and can be added to make -5. The only two numbers that can do that are -7 and 2. So our solution will be (x-7)(x+2) the answer can be checked to determine if it is correct by using the foil method.

AGENDA

I. Bell ringer

II. Review Factoring and Properties of Parabolas

OBJECTIVE

Students will find zeros and vertex of a parabola and accurately factor it.

BIG PICTURE

Parabolas model objects in motion.

MORE EXAMPLES OF CLASS WORK, ETC

Example 3: (x2-16) this is an example of the Difference of 2 Squares. Why? Because (x-4)(x+4) make (x2-16). 4 and -4 are the squares of 16.

Example 4: (x-5)(x2+4x+4). To solve use distributed property. Meaning; multiply the 1st term in the 1st set by the 1st term in the second set. the end of this part should result in x3+4x2+4x then multiply it by the second term in the 1st set. Then by the third.. Then multiple 2nd term in 1st set by the 1st term in the second set followed by the second term and lastly the third. The result of this should be -5x2-20x-20 Finally you add both your results. your combined result should be. x3-x2-16x-20.

Example 5: x2+4x+4 = Perfect Square. Why? because (x+2)(x+2) results in that answer and 2 is the square of 4.

Example 6: Another Perfect Square: 4x2+20x+25. Why because of 5 duh! (3x+5)(2x+5)

Confused so far? An Explanation of Perfect Squares is

Coming your way......

Is It A Perfect Square?????

To determine if it is indeed a perfect square take the square root of the 1st number and multiply it by the square root of the last number then double the result. If the doubled result gives you the number in the middle then *drumroll* IT IS A PERFECT SQUARE.

WARNING/DISCLAIMER: Do not attempt in problems that do not have 3 numbers.

Anyway.... Example:

16x2+48x+36

ARE YOU SERIOUS THE KEYBOARD DOES NOT HAVE A SQUARE ROOT KEY. THE CALCULATOR HAS ONE. AAAAARRRGHH!!!

Anyway... let's continue. We know that the square root of 16 is 4 and the square root of 36 is 6. Next we multiply 6 and 4 and get 24. Then we double and get 48. 48 is the number in the middle therefor it is a Perfect Square.

NOT PERFECT SQUARES:

Quadratic formula: -b +/- square root of (b2-4ac/2)

Example: 9x2+8x+4 (a is in orange, b is in blue c is in red

Plug in the example and your answer should be.......

AN IMPOSSIBLE ONE! IF YOU GOT AN ANSWER YOU ARE INCORRECT!!!!!

Get the Calculator You'll need it for this one!

(we are graphing now. OH! the joy)

Go to y=

Plug In y= 9x2+8x+4

Click Graph

You'll see a Parabola. Not touching the zero

WOW!!! How Fancy

HOMEWORK

Page 251 #1.

Questions of the day (My Favorite Part of the Segment)

1. List a Perfect Square. That was NOT used as an example on this blog post.

2. Factorize: (x+5)(x-5+25)

Well Now this was fun! Wont be doing this again anytime soon. YAY!!!!!

-Lisette Garcia