Remove the Greatest Monomial Factor
Check for the Difference of Two Squares
Check for a Perfect Square Trinomial
Factor x2+bx+c
Factor ax2+bx+cFactor by Grouping
ALWAYS FACTOR COMPLETELY!
We skipped Step 3 because we will be missing many students who are going to a leadership conference. We will do it tomorrow.
p.276 (1,3,5,23,25,31,37,57)
19 comments:
Journal entry 11/17/10
Today in Mr. Gerson's 3rd period class, he introduced the diamond to help us do the 4th step in his "Factoring Algorithm" list. To do this in a problem such as:
x²+ 13x+ 36
the "13" would go in the bottom square of the diamond, and the "36"
on the top. You would have to find which numbers have a product of 36 and a sum of 13. The answer would be nine and four, which would go into the left and right sqaures of the diamond. The answer would be:
(x+9)(x+4)
the "x"s came from x² and the nine and four came from the left and right spaces of the diamond.
i was absent today be cause i was sick i have a question is the assignment the same for all periods? or does 4th per have different assignments ?
sean per 4 has same assignments.
Journal Entry 11/17/10 by Willy Wang
Part 1
Today we learned about step 4 in the Factoring Algorithm list, which was "Factor x²+bx+c. We had to skip step 3 because it was less important. Mr. Gerson taught us to use the "diamond (◊)" method in order to solve the problems. The diamond would be separated into 4 smaller diamonds by drawing 2 lines through the center that are perpendicular, or cross at a right angle.
When solving a problem, such as 4x²+6x+8, you would first factor the first term,which s 4x². The answer should now look like: (2x+?)(2x+?). Second, put 6 in the lowest bottom square of the diamond. Then put 8 in the highest top square of the diamond. There should be 2 squares still empty in the middle. The product of the 2 squares should equal the top square, which is 8. The sum of the 2 squares should be the bottom square, which is 6. The only answer that can fit inside the squares are 2 and 4. 2X4=8 (top square. 2+4=6 (bottom square). Now substituted 2 for one of the ? and 6 for the other. Your answer should be (2x+4)(2x+2).
That was a long journal entry!
11/17/10
Today in Mr Gerson's class were discussed dimond problems.This was the 4th step in the algorithm and we skiped the 3rd step. You split the dimond in to 4 parts with a "x". Two numbers go on the right and left, and the product on the top and sum on the bottom.
ie x^2+4x-12 -12
6 -2
4
the answer is (x+6)(x+2). you must always put greater value first.
the example came out wrong...
Journal Entry 11/17/10 by Willy Wang
Part 2
PRACTICE EXAMPLE 1: x²+13x+36
steps:
1) factor out x². answer as of step 1: (x+?)(x+?)
2) use diamond method. put 13 on the bottom most square and 36 on the top most square. Because 9*4=36 and 9+4=13, 9 and 4 should go into the middle squares. Replace the ?.
ANSWER: (x+9)(x+4)
PRACTICE EXAMPLE 2: x²+4x-12
steps:f
1) factor out x². answer as of step 1: (x+?)(x-?)
2) use diamond method. put 4 on the bottom most square and -12 on the top most square. Because 6*-2=-12 and 6+(-2)=4, 6 and -2 should go into the middle squares. Replace the ?.
ANSWER: (x+6)(x-5)
Journal Entry 11/17/10
Today in class, Mr. Gerson taught us how to use a diamond to help us factor. This is the fourth step in his Factoring Algorithm.
For example, in the problem x²+8x+12, 8 would go in the bottom square and 12 would go in the top square.
The answer would be 6 and 2, which would go in the remaining two squares. The answer would be : (x+6)(x+4).
Journal Entry 11/17/10 by Willy Wang
Part 3
CHALLENGE QUESTION (that i made up myself. try it!)
x³+4x²-32x
steps:
1) use step 1 in the factoring algorithm list (remove greatest monomial factor). You can remove from all of the terms.
answer as of step 1: x(x²+4x-32)
2.1)use step 4 in the factoring algorithm list (factor x²+bx+c).
First factor x². x*x=x². Answer as of step 2.1: x(x+?)(x-?)
2.2) Use the DIAMOND METHOD. Put 4 on the bottom and -32 on the top. Since 8*-4=-32 and 8+(-4)=4, 8 and -4 should go in the middle boxes and replace the ?. Answer as of step 2.2: x(x+8)(x-4)
3)check if you are factored completely. and you are, so the answer is...
ANSWER: x(x+8)(x-4)
i have the longest journal entry! all 3 parts!! sorry about the spelling and stuff in them though :\
that hw was so easy!!!!! i finished it in class
Today, in class we learned how to factor with diamonds. For example, x^2-9x+20
There are four squares on the diamond. On the top,it would be 20.On the bottom, we would put the -9on the bottom. Since the bottom is used for the sum, and the top is the product of the two numbers on the side. Therefore, the two numbers would be -4 and -5.
so the final answer would be
(x-4)(x-5)
Ashley Kim Period 6
Willy, you didn't really have to make yours that long
Period 2:
Period 3: Taylor M.
Period 4: Robert L. & Willy W.
Period 5:
Period 6: Kathrine V. & Ashley K.
where are all the other entries?
Obviously not here yet.
No one else seriously?
Mr.Gerson, when will there be another studyisland assignment?
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