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In school, students may be taught different ways to factor the trinomial $$ax^2+bx+c$$ where $a \neq 1,0$. Possible methods include the classic Guess and Check Method, Grouping, Box Method, and the Snowflake Method, which is the one I'm focused on right now. If the Snowflake Method is used correctly, factoring trinomials can happen much quicker than using the traditional Guess and Check Method.

Indeed, the Snowflake Method works for factoring the following trinomial: $$5x^2-x-18$$ First we set up the snowflake: enter image description here

To briefly summarize, we label and fill in the "wings" as seen above. Then we find the factors of $c$ that add to $b$ and multiply to $ac$ and put them in the empty wings. This creates fractions which I circled, and they must be reduced if possible. This gives us the correct factored form of $\boxed{(x-2)(5x+9)}$.

Now, here is my problem.

I tried to use the Snowflake Method to factor $$7x^2+37x+36$$ I set up the snowflake as follows: enter image description here

There was no "nice" factor pair here because no pair multiplied to get $ac=252$. However, I noticed that $(7)(36)=252$, so I chose the pair $(36,1)$. This would imply that the factored form is $$(7x+36)(7x+1)$$ but clearly this is incorrect. The answer should be $$(7x+9)(x+4)$$ I don't see how the Snowflake Method can produce this. It seems to impossible to produce the $(x+4)$ term because if we divide $7$ by any of the factors of $36$, we will not get $4$.

I would like to understand: Why did the Snowflake Method not work for this example? Is there some restriction when using the Snowflake Method that I missed?

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    $\begingroup$ I would be interested to know in which countries this method is taught. In the U.S. ? In U.K. ? it is completely unknown in my country (France). $\endgroup$
    – Jean Marie
    Aug 18, 2020 at 18:54
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    $\begingroup$ It's my understanding that this method is rarely taught in schools. I think the Box Method is actually more commonly used by teachers. Personally, I like the Snowflake Method because it sets a clear, defined solution pathway, whereas Guess and Check may take more time depending on the coefficients in the trinomial. $\endgroup$
    – FoiledIt24
    Aug 18, 2020 at 20:15

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Two numbers, say $p$ and $q$, $p+q=37$, $p×q=252$, so $p=28$ and $q=9$. So they are not $36$ and $1$. Then it will work.

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  • $\begingroup$ So it would appear that I must add this step when using the Snowflake Method $\endgroup$
    – FoiledIt24
    Aug 18, 2020 at 19:37

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