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What number goes in the question mark so that the quadratic is the square of a binomial? 9x^2 +6x+?

 

PLEASE ANSWER THANK YOU SO MUCH :)!

 Mar 3, 2021
 #1
avatar+34395 
+1

(3x+1)^2 =   9x^2 + 6x + 1

 Mar 3, 2021
 #2
avatar+9313 
+3

Let  m  be the mystery number.

 

9x2 + 6x + m  =  (3x)2 + 2(3x) + m

 

Now we can substitute  a  for  3x  like this:

 

a2 + 2a + m

 

Now we don't have to worry about the coefficient of  9  on the first term....and so  m  is half the coefficient of the middle term squared.

 

m  =  ((1/2) * 2)^2   =   1^2   =   1

 

 

Check:

 

9x2 + 6x + 1   =   (3x + 1)(3x + 1)   =   (3x + 1)2

 Mar 3, 2021

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