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Find the number that we can place in the box, so that the resulting expression can be factored as the product of two linear factors.
\(3mn - 6m + 5n + \boxed{\phantom{00}}\)

 

Thank you! :D

 Apr 19, 2020
 #1
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Hi floccinaucini! 

 

So, we can start by noticing the signs. All of the signs are positive except for the \(-6m\). So, that means that \(m\) is multiplied by a negative number. 

 

What we know right now: \((\text{_}m+\text{_})(\text{_}n-\text{_})\). (The _ are to symbolize the numbers we don't know.)

 

Since we know that we have a \(5n\) term, we know that 5 goes in the black space next to m. Now we have \((\text{_}m+5)(\text{_}n-\text{_})\).

We also have a \(3mn\) term, so let's put the 3 next to m. Now we have \((3m+5)(\text{_}n-\text{_})\)

We also have a \(6m\) term, so we know that something multiplied by 3m = 6m. \(\frac{6m}{3m}=2\). Now we have  \((3m+5)(n-2)\)

 

Now, we have covered all the terms. So let's multiply the factors out to find out what \(\square\) is!

3m*n=3mn

3m*-2=-6m

5*n=5n

5*-2=-10

 

So they multiply to \(3mn-6m+5n-10\). And now we can clearly that \(\square = -10\)!

 

I hoped this helped you floccinaucini!

:)

\(\)

.
 Apr 19, 2020

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