Question 214885
I need help factoring out this equation: {{{9x^2+6x+1}}}


Step 1.  We need to find two integers m & n  that their product is mn=ac=9 where a=9 and b=6 and their sum m+n=6.


Step 2.  After trial an error the integers are m=n=3.  Then based on the method of grouping where 6x=3x+3x based on the integers m & n, we have


{{{9x^2+6x+1=(9x^2+3x)+1*(3x+1)}}}

Step 3.  Factoring 3x out of the first group we have


{{{9x^2+6x+1=3x*(3x+1)+1*(3x+1)}}}


Step 4.  Now factor (3x+1) from both groups since it's common to both of them.


{{{9x^2+6x+1=(3x+1)(3x+1)}}}  ANSWER


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J