# 9.6 Factoring Trinomials where the leading coefficient is NOT 1
- AWP (Algebra with Pizazz) wksht. pg. 91
- (1-17) all
- paper must be folded into boxes
- heading MUST include both the question (What Happened When the Boarding House Blew Up?" and the answer to the question.
The following problem is # 1 from the worksheet (^ means raised to some power):
1. To factor 3x^2 + 7x + 2:
First, do a product and sum chart. Remember that the product is found by multiplying the first and last numbers together. The sum is always the middle #. So, for this problem, our product would be 3 times 2 which equals 6. Our sum is 7. Now factor 6. You could have eitther 1 times 6 or 2 times 3. Both equal 6 when mutliplied together, but only one pair will equal 7 when added together. That's right! Our Bingo! numbers are 1 and 6.
Now that we have our Bingo! numbers, bring down the first and the last terms:
3x^2 +___ + ____ +2
Split the middle term of 7x with your bingo numbers:
3x^2 +6x + 1x +2
Now place parentheses around 2 at a time:
(3x^2 + 6x) + (1x + 2)
Now find the GCF for each group and factor it:
3x (x +2) + 1 (x+2)
Make sure that the factor in the parentheses are the same. If not, go back to the drawing board. In this case, both pairs of parentheses are the same since they both say (x+2).
Now, you're ready to write your final answer. You'll have 2 factors or 2 pairs of parentheses. Fill in one of them with your blue GCFs and the other one is the common one in black:
(3x+1) (x+2)
Now look for both of these factors in the answer columns. The 3x+1 factor has an 8 next to it. The x+2 factor has the letter W next to it. That means that you fill in "W" for box #8 at the bottom of the worksheet to figure out the answer to "What Happened When the Boarding House Blew Up?".
Let's make this interesting. I will give 10 extra credit points to the first person who figures out a problem correctly. ***10 points max per student***. To get the 10 extra credit points, you must EXPLAIN your solution like I did above. No explanation = no extra credit. Once a problem has been explained, the extra credit for that problem is gone. You must do a different problem. However, the problem is NOT off the market until I, msichan, says it is. So, you're best bet is to post a solution even if someone else has already posted one for that problem. He or she could be wrong or the explanation may have some holes in it.
***If, by 8 p.m., all the extra credit has not been handed out, then those of you who already received 10 extra credit points can go for another 10. Good Luck! Have fun!
