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Thanks for your help btw!

fill in the blank so that the resulting exxpression can be factored as the product of the two linear equations \(2 m n − 21 m + 6 n + blank\)

 Dec 9, 2023
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We need to find a value that, when added to the expression, allows it to be factored into the product of two linear equations. The given expression is 2mn - 21m + 6n.

 

We can start by factoring out a common factor of 2m from the first two terms and a common factor of 6 from the last two terms:

2mn - 21m + 6n = 2m(n - 11) + 6(n - 1)

 

Now, we need to find a value to add that allows us to factor out a common factor of (n - 1) from the entire expression. This means we need to find a value that is a multiple of (n - 1) and that can be added to the current expression without changing its value.

 

One such value is -22. Adding this to the expression, we get:

2mn - 21m + 6n - 22 = 2m(n - 11) + 6(n - 1) - 22

 

Now we can factor out (n - 1):

2m(n - 11) + 6(n - 1) - 22 = (n - 1)(2m - 12 + 6n - 6)

 

Therefore, the missing term is -22.

 Dec 10, 2023

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