You can
put this solution on YOUR website!This is what I call "Advanced Trinomial Factoring". It might NOT be a lesson in algebra.com, but you can find a lengthy explanation of this in my book at my website. Click on my user name "rapaljer" anywhere in algebra.com. Then click on "Basic Algebra", then "Samples of Basic Algebra: One Step at a Time", go to "Chapter 2", and look for "Advanced Trinomial Factoring."
Now, having given that notice for my free website,
15X^2+19X+6=0
It pretty much has to start with
(5x _____ )(3x _____ ) = 0
Now, look at the last times last, which has to end up with a +6. That would most likely have to be 3 times 2, or 2 times 3. Now, try putting the 3 in the first set of parentheses and the 2 in the second set of parentheses. In my chapter on this topic, I explain how I knew to do that in more detail. For now it looks like this:
(5x___ 3)(3x ___ 2) = 0.
Now do the outer times outer and inner times inner and see if it adds up to 19x. Outer times outer = 10x; inner times inner = 9x; and sure enough it adds up to 19x.
(5x+3)(3x+2) = 0
First solution:
5x+3 = 0
5x= -3
Second solution:
3x+2 = 0
3x= -2
R^2 at SCC
You can
put this solution on YOUR website!Use what is called the "AC Method" to factor this trinomial
In your problem a=15, b=19, c=6
Form the product ac= 90
Notice that b= 19
Now find two numbers whose product is 90 and whose sum is 19.
They are 9 and 10.
Rewrite your problem, substituting 9x + 10x in place of 19x
to get the following:
15x^2 +9x +10x +6
Now factor the 1st two terms and then the last two terms as follows:
3x(5x+3)2(5x+3)
= (5x+3)(3x+2
By the way. If there are not two numbers whose product is AC and
whose sum is B you will have to use the binomial formula to find
the factors.
Cheers,
Stan H.
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